Word problems worked out.

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.