The problem involves a coin bank containing pennies and nickels totaling $17.00. There are 1140 coins in the bank. Letting x=pennies and y=nickels, two equations are set up: x+y=1140 for the total coins, and 17=0.01x+0.05y for the total value. Solving the system of equations determines how many of each coin are in the bank.
Keynote delivered at LSU Center for Computation and Technology's Virtual Worlds: New Realms for Culture, Creativity, Commerce, Computation, and Communication Conference.
Keynote delivered at LSU Center for Computation and Technology's Virtual Worlds: New Realms for Culture, Creativity, Commerce, Computation, and Communication Conference.
1. p. 358/9 Janet is mixing a 15% glucose solution with a 35% glucose solution.
This mixture produces 35 liters of a solution that contains 6 liters of pure
glucose (100% solution). How many liters of each solution is Janet using in the
mixture?
2. p. 358/9 Janet is mixing a 15% glucose solution with a 35% glucose solution.
This mixture produces 35 liters of a solution that contains 6 liters of pure
glucose (100% solution). How many liters of each solution is Janet using in the
mixture?
Make a table to represent the information:
3. p. 358/9 Janet is mixing a 15% glucose solution with a 35% glucose solution.
This mixture produces 35 liters of a solution that contains 6 liters of pure
glucose (100% solution). How many liters of each solution is Janet using in the
mixture?
Make a table to represent the information:
# of liters of solution # of liters of glucose
15% solution x 0.15x
35% solution y 0.35y
mixture 35 6
4. p. 358/9 Janet is mixing a 15% glucose solution with a 35% glucose solution.
This mixture produces 35 liters of a solution that contains 6 liters of pure
glucose (100% solution). How many liters of each solution is Janet using in the
mixture?
Make a table to represent the information:
# of liters of solution # of liters of glucose
15% solution x 0.15x
35% solution y 0.35y
mixture 35 6
x + y = 35
0.15x + 0.35y = 6
5. p. 358/9 Janet is mixing a 15% glucose solution with a 35% glucose solution.
This mixture produces 35 liters of a solution that contains 6 liters of pure
glucose (100% solution). How many liters of each solution is Janet using in the
mixture?
Make a table to represent the information:
# of liters of solution # of liters of glucose
15% solution x 0.15x
35% solution y 0.35y
mixture 35 6
x + y = 35
0.15x + 0.35y = 6
(31.25, 3.75)
6. p. 358/9 Janet is mixing a 15% glucose solution with a 35% glucose solution.
This mixture produces 35 liters of a solution that contains 6 liters of pure
glucose (100% solution). How many liters of each solution is Janet using in the
mixture?
Make a table to represent the information:
# of liters of solution # of liters of glucose
15% solution x 0.15x
35% solution y 0.35y
mixture 35 6
x + y = 35
0.15x + 0.35y = 6
So, 31.25 liters of the 15%
(31.25, 3.75)
solution and 3.75 liters of
the 35% solution.
7. p. 358/10 Catherine is camping along a river. It takes her 1.5 hours to paddle
her canoe 6 miles upstream from her campsite. Catherine turns her canoe
around a returns 6 miles downstream to her campsite in exactly 1 hour. What is
the rate of the river’ current and the rate of Catherine’ paddling in still water?
s s
8. p. 358/10 Catherine is camping along a river. It takes her 1.5 hours to paddle
her canoe 6 miles upstream from her campsite. Catherine turns her canoe
around a returns 6 miles downstream to her campsite in exactly 1 hour. What is
the rate of the river’ current and the rate of Catherine’ paddling in still water?
s s
Let x represent the rate of Catherine’ paddling in still water.
s
9. p. 358/10 Catherine is camping along a river. It takes her 1.5 hours to paddle
her canoe 6 miles upstream from her campsite. Catherine turns her canoe
around a returns 6 miles downstream to her campsite in exactly 1 hour. What is
the rate of the river’ current and the rate of Catherine’ paddling in still water?
s s
Let x represent the rate of Catherine’ paddling in still water.
s
Let y represent the speed of the river’s current.
10. p. 358/10 Catherine is camping along a river. It takes her 1.5 hours to paddle
her canoe 6 miles upstream from her campsite. Catherine turns her canoe
around a returns 6 miles downstream to her campsite in exactly 1 hour. What is
the rate of the river’ current and the rate of Catherine’ paddling in still water?
s s
Let x represent the rate of Catherine’ paddling in still water.
s
Let y represent the speed of the river’s current.
So x + y represents the speed of her paddling with the current.
11. p. 358/10 Catherine is camping along a river. It takes her 1.5 hours to paddle
her canoe 6 miles upstream from her campsite. Catherine turns her canoe
around a returns 6 miles downstream to her campsite in exactly 1 hour. What is
the rate of the river’ current and the rate of Catherine’ paddling in still water?
s s
Let x represent the rate of Catherine’ paddling in still water.
s
Let y represent the speed of the river’s current.
So x + y represents the speed of her paddling with the current.
So x - y represents the speed of her paddling against the current.
12. p. 358/10 Catherine is camping along a river. It takes her 1.5 hours to paddle
her canoe 6 miles upstream from her campsite. Catherine turns her canoe
around a returns 6 miles downstream to her campsite in exactly 1 hour. What is
the rate of the river’ current and the rate of Catherine’ paddling in still water?
s s
Let x represent the rate of Catherine’ paddling in still water.
s
Let y represent the speed of the river’s current.
So x + y represents the speed of her paddling with the current.
So x - y represents the speed of her paddling against the current.
Remember that distance = speed x time & make your system:
13. p. 358/10 Catherine is camping along a river. It takes her 1.5 hours to paddle
her canoe 6 miles upstream from her campsite. Catherine turns her canoe
around a returns 6 miles downstream to her campsite in exactly 1 hour. What is
the rate of the river’ current and the rate of Catherine’ paddling in still water?
s s
Let x represent the rate of Catherine’ paddling in still water.
s
Let y represent the speed of the river’s current.
So x + y represents the speed of her paddling with the current.
So x - y represents the speed of her paddling against the current.
Remember that distance = speed x time & make your system:
6 = (x + y)
6 = (x − y)1.5
14. p. 358/10 Catherine is camping along a river. It takes her 1.5 hours to paddle
her canoe 6 miles upstream from her campsite. Catherine turns her canoe
around a returns 6 miles downstream to her campsite in exactly 1 hour. What is
the rate of the river’ current and the rate of Catherine’ paddling in still water?
s s
Let x represent the rate of Catherine’ paddling in still water.
s
Let y represent the speed of the river’s current.
So x + y represents the speed of her paddling with the current.
So x - y represents the speed of her paddling against the current.
Remember that distance = speed x time & make your system:
6 = (x + y)
6 = (x − y)1.5
(5, 1)
15. p. 358/10 Catherine is camping along a river. It takes her 1.5 hours to paddle
her canoe 6 miles upstream from her campsite. Catherine turns her canoe
around a returns 6 miles downstream to her campsite in exactly 1 hour. What is
the rate of the river’ current and the rate of Catherine’ paddling in still water?
s s
Let x represent the rate of Catherine’ paddling in still water.
s
Let y represent the speed of the river’s current.
So x + y represents the speed of her paddling with the current.
So x - y represents the speed of her paddling against the current.
Remember that distance = speed x time & make your system:
6 = (x + y)
6 = (x − y)1.5
So, the canoe goes 5 mph (5, 1)
and the current goes 1 mph.
16. p. 358/11 The coin box of a vending machine contains 6 times as many quarters
as dimes. If the total amount of money in quarters and dimes is $28.80, how
many quarters and how many dimes are in the box?
17. p. 358/11 The coin box of a vending machine contains 6 times as many quarters
as dimes. If the total amount of money in quarters and dimes is $28.80, how
many quarters and how many dimes are in the box?
Let x represent the number of quarters in the box
18. p. 358/11 The coin box of a vending machine contains 6 times as many quarters
as dimes. If the total amount of money in quarters and dimes is $28.80, how
many quarters and how many dimes are in the box?
Let x represent the number of quarters in the box
Let y represent the number of dimes in the box
19. p. 358/11 The coin box of a vending machine contains 6 times as many quarters
as dimes. If the total amount of money in quarters and dimes is $28.80, how
many quarters and how many dimes are in the box?
Let x represent the number of quarters in the box
Let y represent the number of dimes in the box
Since each quarter is worth 25 cents, the x quarters are
worth 0.25x dollars, and since each dime is worth 10 cents,
the y dimes are worth 0.1y dollars.
20. p. 358/11 The coin box of a vending machine contains 6 times as many quarters
as dimes. If the total amount of money in quarters and dimes is $28.80, how
many quarters and how many dimes are in the box?
Let x represent the number of quarters in the box
Let y represent the number of dimes in the box
Since each quarter is worth 25 cents, the x quarters are
worth 0.25x dollars, and since each dime is worth 10 cents,
the y dimes are worth 0.1y dollars.
Use the first sentence to make one equation and the total
value $28.80 to make another. Be careful, though- which
variable is multiplied by 6?!?
21. p. 358/11 The coin box of a vending machine contains 6 times as many quarters
as dimes. If the total amount of money in quarters and dimes is $28.80, how
many quarters and how many dimes are in the box?
Let x represent the number of quarters in the box
Let y represent the number of dimes in the box
Since each quarter is worth 25 cents, the x quarters are
worth 0.25x dollars, and since each dime is worth 10 cents,
the y dimes are worth 0.1y dollars.
Use the first sentence to make one equation and the total
value $28.80 to make another. Be careful, though- which
variable is multiplied by 6?!?
x = 6y
28.80 = 0.25x + 0.1y
22. p. 358/11 The coin box of a vending machine contains 6 times as many quarters
as dimes. If the total amount of money in quarters and dimes is $28.80, how
many quarters and how many dimes are in the box?
Let x represent the number of quarters in the box
Let y represent the number of dimes in the box
Since each quarter is worth 25 cents, the x quarters are
worth 0.25x dollars, and since each dime is worth 10 cents,
the y dimes are worth 0.1y dollars.
Use the first sentence to make one equation and the total
value $28.80 to make another. Be careful, though- which
variable is multiplied by 6?!?
x = 6y
28.80 = 0.25x + 0.1y
(108, 18)
23. p. 358/11 The coin box of a vending machine contains 6 times as many quarters
as dimes. If the total amount of money in quarters and dimes is $28.80, how
many quarters and how many dimes are in the box?
Let x represent the number of quarters in the box
Let y represent the number of dimes in the box
Since each quarter is worth 25 cents, the x quarters are
worth 0.25x dollars, and since each dime is worth 10 cents,
the y dimes are worth 0.1y dollars.
Use the first sentence to make one equation and the total
value $28.80 to make another. Be careful, though- which
variable is multiplied by 6?!?
x = 6y
28.80 = 0.25x + 0.1y
So, 108 quarters (108, 18)
and 18 dimes.
24. p. 358/16 A coin bank contains $17.00 in pennies and nickels. If there are 1140
coins in the bank, how many of the coins are nickels?
25. p. 358/16 A coin bank contains $17.00 in pennies and nickels. If there are 1140
coins in the bank, how many of the coins are nickels?
Let x represent the number of pennies in the bank.
26. p. 358/16 A coin bank contains $17.00 in pennies and nickels. If there are 1140
coins in the bank, how many of the coins are nickels?
Let x represent the number of pennies in the bank.
Let y represent the number of nickels in the bank.
27. p. 358/16 A coin bank contains $17.00 in pennies and nickels. If there are 1140
coins in the bank, how many of the coins are nickels?
Let x represent the number of pennies in the bank.
Let y represent the number of nickels in the bank.
Since each penny is worth 1 cent, the x pennies are worth
0.01x dollars, and since each nickel is worth 5 cents, the y
nickels are worth 0.05y dollars.
28. p. 358/16 A coin bank contains $17.00 in pennies and nickels. If there are 1140
coins in the bank, how many of the coins are nickels?
Let x represent the number of pennies in the bank.
Let y represent the number of nickels in the bank.
Since each penny is worth 1 cent, the x pennies are worth
0.01x dollars, and since each nickel is worth 5 cents, the y
nickels are worth 0.05y dollars.
Use the total number 1140 to make one equation and the
total value $17.00 to make another.
29. p. 358/16 A coin bank contains $17.00 in pennies and nickels. If there are 1140
coins in the bank, how many of the coins are nickels?
Let x represent the number of pennies in the bank.
Let y represent the number of nickels in the bank.
Since each penny is worth 1 cent, the x pennies are worth
0.01x dollars, and since each nickel is worth 5 cents, the y
nickels are worth 0.05y dollars.
Use the total number 1140 to make one equation and the
total value $17.00 to make another.
x + y = 1140
17.00 = 0.01x + 0.05y
30. p. 358/16 A coin bank contains $17.00 in pennies and nickels. If there are 1140
coins in the bank, how many of the coins are nickels?
Let x represent the number of pennies in the bank.
Let y represent the number of nickels in the bank.
Since each penny is worth 1 cent, the x pennies are worth
0.01x dollars, and since each nickel is worth 5 cents, the y
nickels are worth 0.05y dollars.
Use the total number 1140 to make one equation and the
total value $17.00 to make another.
x + y = 1140
17.00 = 0.01x + 0.05y
(1000, 140)
31. p. 358/16 A coin bank contains $17.00 in pennies and nickels. If there are 1140
coins in the bank, how many of the coins are nickels?
Let x represent the number of pennies in the bank.
Let y represent the number of nickels in the bank.
Since each penny is worth 1 cent, the x pennies are worth
0.01x dollars, and since each nickel is worth 5 cents, the y
nickels are worth 0.05y dollars.
Use the total number 1140 to make one equation and the
total value $17.00 to make another.
x + y = 1140
17.00 = 0.01x + 0.05y
So, there are 140 (1000, 140)
nickels.
32. p. 358/18 How many ounces of a 20% salt solution should be mixed with a 10%
salt solution to produce 45 ounces of a 14% salt solution?
33. p. 358/18 How many ounces of a 20% salt solution should be mixed with a 10%
salt solution to produce 45 ounces of a 14% salt solution?
Make a table to represent the information:
34. p. 358/18 How many ounces of a 20% salt solution should be mixed with a 10%
salt solution to produce 45 ounces of a 14% salt solution?
Make a table to represent the information:
# of ounces of solution # of ounces of salt
20% solution x 0.2x
10% solution y 0.1y
14% solution 45 (0.14)(45)
35. p. 358/18 How many ounces of a 20% salt solution should be mixed with a 10%
salt solution to produce 45 ounces of a 14% salt solution?
Make a table to represent the information:
# of ounces of solution # of ounces of salt
20% solution x 0.2x
10% solution y 0.1y
14% solution 45 (0.14)(45)
x + y = 45
0.2x + 0.1y = (0.14)(45)
36. p. 358/18 How many ounces of a 20% salt solution should be mixed with a 10%
salt solution to produce 45 ounces of a 14% salt solution?
Make a table to represent the information:
# of ounces of solution # of ounces of salt
20% solution x 0.2x
10% solution y 0.1y
14% solution 45 (0.14)(45)
x + y = 45
0.2x + 0.1y = (0.14)(45) (18, 27)
37. p. 358/18 How many ounces of a 20% salt solution should be mixed with a 10%
salt solution to produce 45 ounces of a 14% salt solution?
Make a table to represent the information:
# of ounces of solution # of ounces of salt
20% solution x 0.2x
10% solution y 0.1y
14% solution 45 (0.14)(45)
x + y = 45
0.2x + 0.1y = (0.14)(45) (18, 27)
So, 18 ounces of the 20%
solution and 27 ounces of
the 10% solution.
38. p. 358/19 A 4% salt solution is mixed with a 16% salt solution. How many
milliliters of each solution are needed to obtain 600 milliliters of a 10% solution?
39. p. 358/19 A 4% salt solution is mixed with a 16% salt solution. How many
milliliters of each solution are needed to obtain 600 milliliters of a 10% solution?
Make a table to represent the information:
40. p. 358/19 A 4% salt solution is mixed with a 16% salt solution. How many
milliliters of each solution are needed to obtain 600 milliliters of a 10% solution?
Make a table to represent the information:
# of ml of solution # of ml of salt
4% solution x 0.04x
16% solution y 0.16y
10% solution 600 (0.1)(600)
41. p. 358/19 A 4% salt solution is mixed with a 16% salt solution. How many
milliliters of each solution are needed to obtain 600 milliliters of a 10% solution?
Make a table to represent the information:
# of ml of solution # of ml of salt
4% solution x 0.04x
16% solution y 0.16y
10% solution 600 (0.1)(600)
x + y = 600
0.04x + 0.16y = (0.1)(600)
42. p. 358/19 A 4% salt solution is mixed with a 16% salt solution. How many
milliliters of each solution are needed to obtain 600 milliliters of a 10% solution?
Make a table to represent the information:
# of ml of solution # of ml of salt
4% solution x 0.04x
16% solution y 0.16y
10% solution 600 (0.1)(600)
x + y = 600
0.04x + 0.16y = (0.1)(600) (300, 300)
43. p. 358/19 A 4% salt solution is mixed with a 16% salt solution. How many
milliliters of each solution are needed to obtain 600 milliliters of a 10% solution?
Make a table to represent the information:
# of ml of solution # of ml of salt
4% solution x 0.04x
16% solution y 0.16y
10% solution 600 (0.1)(600)
x + y = 600
0.04x + 0.16y = (0.1)(600) (300, 300)
So, 300 ml of each solution.
44. p. 358/20 With a tailwind, a jet flew 2000 miles in 4 hours, but the return
trip against the same wind required 5 hours. Find the jet’s speed and the wind
speed.
45. p. 358/20 With a tailwind, a jet flew 2000 miles in 4 hours, but the return
trip against the same wind required 5 hours. Find the jet’s speed and the wind
speed.
Let x represent the jet’ speed.
s
46. p. 358/20 With a tailwind, a jet flew 2000 miles in 4 hours, but the return
trip against the same wind required 5 hours. Find the jet’s speed and the wind
speed.
Let x represent the jet’ speed.
s
Let y represent the wind speed.
47. p. 358/20 With a tailwind, a jet flew 2000 miles in 4 hours, but the return
trip against the same wind required 5 hours. Find the jet’s speed and the wind
speed.
Let x represent the jet’ speed.
s
Let y represent the wind speed.
So x + y represents the speed with the tailwind.
48. p. 358/20 With a tailwind, a jet flew 2000 miles in 4 hours, but the return
trip against the same wind required 5 hours. Find the jet’s speed and the wind
speed.
Let x represent the jet’ speed.
s
Let y represent the wind speed.
So x + y represents the speed with the tailwind.
So x - y represents the speed against the wind.
49. p. 358/20 With a tailwind, a jet flew 2000 miles in 4 hours, but the return
trip against the same wind required 5 hours. Find the jet’s speed and the wind
speed.
Let x represent the jet’ speed.
s
Let y represent the wind speed.
So x + y represents the speed with the tailwind.
So x - y represents the speed against the wind.
Remember that distance = speed x time & make your system:
50. p. 358/20 With a tailwind, a jet flew 2000 miles in 4 hours, but the return
trip against the same wind required 5 hours. Find the jet’s speed and the wind
speed.
Let x represent the jet’ speed.
s
Let y represent the wind speed.
So x + y represents the speed with the tailwind.
So x - y represents the speed against the wind.
Remember that distance = speed x time & make your system:
2000 = (x + y)4
2000 = (x − y)5
51. p. 358/20 With a tailwind, a jet flew 2000 miles in 4 hours, but the return
trip against the same wind required 5 hours. Find the jet’s speed and the wind
speed.
Let x represent the jet’ speed.
s
Let y represent the wind speed.
So x + y represents the speed with the tailwind.
So x - y represents the speed against the wind.
Remember that distance = speed x time & make your system:
2000 = (x + y)4
2000 = (x − y)5
(450, 50)
52. p. 358/20 With a tailwind, a jet flew 2000 miles in 4 hours, but the return
trip against the same wind required 5 hours. Find the jet’s speed and the wind
speed.
Let x represent the jet’ speed.
s
Let y represent the wind speed.
So x + y represents the speed with the tailwind.
So x - y represents the speed against the wind.
Remember that distance = speed x time & make your system:
2000 = (x + y)4
2000 = (x − y)5
(450, 50)
So, the jet flies at 450 mph
and the wind speed is 50 mph.
53. p. 358/21 A grocery store sells a mixture of peanuts and raisins for $1.75 per
pound. If peanuts cost $1.25 per pound and raisins cost $2.75 per pound, what
amount of raisins and peanuts go into 1 pound of the mixture?
54. p. 358/21 A grocery store sells a mixture of peanuts and raisins for $1.75 per
pound. If peanuts cost $1.25 per pound and raisins cost $2.75 per pound, what
amount of raisins and peanuts go into 1 pound of the mixture?
Make a table to represent the information:
55. p. 358/21 A grocery store sells a mixture of peanuts and raisins for $1.75 per
pound. If peanuts cost $1.25 per pound and raisins cost $2.75 per pound, what
amount of raisins and peanuts go into 1 pound of the mixture?
Make a table to represent the information:
cost per pound # of pounds total cost
peanuts $1.25 x 1.25x
raisins $2.75 y 2.75y
mixture $1.75 1 1.75
56. p. 358/21 A grocery store sells a mixture of peanuts and raisins for $1.75 per
pound. If peanuts cost $1.25 per pound and raisins cost $2.75 per pound, what
amount of raisins and peanuts go into 1 pound of the mixture?
Make a table to represent the information:
cost per pound # of pounds total cost
peanuts $1.25 x 1.25x
raisins $2.75 y 2.75y
mixture $1.75 1 1.75
x + y = 1
1.25x + 2.75y = 1.75
57. p. 358/21 A grocery store sells a mixture of peanuts and raisins for $1.75 per
pound. If peanuts cost $1.25 per pound and raisins cost $2.75 per pound, what
amount of raisins and peanuts go into 1 pound of the mixture?
Make a table to represent the information:
cost per pound # of pounds total cost
peanuts $1.25 x 1.25x
raisins $2.75 y 2.75y
mixture $1.75 1 1.75
x + y = 1
1.25x + 2.75y = 1.75 (2/3, 1/3)
58. p. 358/21 A grocery store sells a mixture of peanuts and raisins for $1.75 per
pound. If peanuts cost $1.25 per pound and raisins cost $2.75 per pound, what
amount of raisins and peanuts go into 1 pound of the mixture?
Make a table to represent the information:
cost per pound # of pounds total cost
peanuts $1.25 x 1.25x
raisins $2.75 y 2.75y
mixture $1.75 1 1.75
x + y = 1
1.25x + 2.75y = 1.75 (2/3, 1/3)
So, 2/3 of a pound of
peanuts and 1/3 of a pound
of raisins.