This document contains summaries of different types of math word problems, including translating word problems, age problems, digit problems, and money problems. It also provides sample word problems and step-by-step solutions for each type. The document was created by several students for a special math project and covers topics commonly seen in math assessments.
Word problem is often used to refer to any mathematical exercise where significant background information on the problem is presented as text rather than in mathematical notation. As word problems often involve a narrative of some sort, they are occasionally also referred to as story problems and may vary in the amount of language used.
-http://en.wikipedia.org/wiki/Word_problem_(mathematics_education)
Pre-Calculus Quarter 4 Exam
Name: _________________________
Score: ______ / ______
1.
Find the indicated sum. Show your work.
2.
Locate the foci of the ellipse. Show your work.
3.
Solve the system by the substitution method. Show your work.
2y - x = 5
x2 + y2 - 25 = 0
4.
Graph the function. Then use your graph to find the indicated limit. You do not have to provide the graph
f(x) = 5x - 3, f(x)
5.
Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists. Show your work.
4x - y + 3z = 12
x + 4y + 6z = -32
5x + 3y + 9z = 20
6.
Solve the system of equations using matrices. Use Gaussian elimination with back-substitution.
x + y + z = -5
x - y + 3z = -1
4x + y + z = -2
7. A woman works out by running and swimming. When she runs, she burns 7 calories per minute. When she swims, she burns 8 calories per minute. She wants to burn at least 336 calories in her workout. Write an inequality that describes the situation. Let x represent the number of minutes running and y the number of minutes swimming. Because x and y must be positive, limit the boarders to quadrant I only.
Short Answer Questions: Type your answer below each question. Show your work.
8.
A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these statements is true. Show your work.
Sn: 12 + 42 + 72 + . . . + (3n - 2)2 =
9.
A statement Sn about the positive integers is given. Write statements Sk and Sk+1, simplifying Sk+1 completely. Show your work.
Sn: 1 ∙ 2 + 2 ∙ 3 + 3 ∙ 4 + . . . + n(n + 1) = [n(n + 1)(n + 2)]/3
10.
Joely's Tea Shop, a store that specializes in tea blends, has available 45 pounds of A grade tea and 70 pounds of B grade tea. These will be blended into 1 pound packages as follows: A breakfast blend that contains one third of a pound of A grade tea and two thirds of a pound of B grade tea and an afternoon tea that contains one half pound of A grade tea and one half pound of B grade tea. If Joely makes a profit of $1.50 on each pound of the breakfast blend and $2.00 profit on each pound of the afternoon blend, how many pounds of each blend should she make to maximize profits? What is the maximum profit?
11
Your computer supply store sells two types of laser printers. The first type, A, has a cost of $86 and you make a $45 profit on each one. The second type, B, has a cost of $130 and you make a $35 profit on each one. You expect to sell at least 100 laser printers this month and you need to make at least $3850 profit on them. How many of what type of printer should you order if you want to minimize your cost?
12
A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these statements is true. Show your work.
Sn: 2 + 5 + .
Pre-Calculus Quarter 4 Exam
1
Name: _________________________
Score: ______ / ______
1. Find the indicated sum. Show your work.
2. Locate the foci of the ellipse. Show your work.
𝑥2
36
+
𝑦2
11
= 1
Pre-Calculus Quarter 4 Exam
2
3. Solve the system by the substitution method. Show your work.
2y - x = 5
x2 + y2 - 25 = 0
4. Graph the function. Then use your graph to find the indicated limit. You do not have to
provide the graph
f(x) = 5x - 3, f(x)
5. Use Gaussian elimination to find the complete solution to the system of equations, or state
that none exists. Show your work.
4x - y + 3z = 12
x + 4y + 6z = -32
5x + 3y + 9z = 20
Pre-Calculus Quarter 4 Exam
3
6. Solve the system of equations using matrices. Use Gaussian elimination with back-
substitution.
x + y + z = -5
x - y + 3z = -1
4x + y + z = -2
7. A woman works out by running and swimming. When she runs, she burns 7 calories per
minute. When she swims, she burns 8 calories per minute. She wants to burn at least 336
calories in her workout. Write an inequality that describes the situation. Let x represent the
number of minutes running and y the number of minutes swimming. Because x and y must be
positive, limit the boarders to quadrant I only.
Short Answer Questions: Type your answer below each question. Show your work.
8. A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that
each of these statements is true. Show your work.
Sn: 1
2
+ 4
2
+ 7
2
+ . . . + (3n - 2)
2
=
𝑛(6𝑛2−3𝑛−1)
2
Pre-Calculus Quarter 4 Exam
4
9. A statement Sn about the positive integers is given. Write statements Sk and Sk+1, simplifying
Sk+1 completely. Show your work.
Sn: 1 ∙ 2 + 2 ∙ 3 + 3 ∙ 4 + . . . + n(n + 1) = [n(n + 1)(n + 2)]/3
10. Joely's Tea Shop, a store that specializes in tea blends, has available 45 pounds of A grade tea and
70 pounds of B grade tea. These will be blended into 1 pound packages as follows: A breakfast
blend that contains one third of a pound of A grade tea and two thirds of a pound of B grade tea
and an afternoon tea that contains one half pound of A grade tea and one half pound of B grade
tea. If Joely makes a profit of $1.50 on each pound of the breakfast blend and $2.00 profit on
each pound of the afternoon blend, how many pounds of each blend should she make to
maximize profits? What is the maximum profit?
11 Your computer supply store sells two types of laser printers. The first type, A, has a cost of $86
and you make a $45 profit on each one. The second type, B, has a cost of $130 and you make a
$35 profit on each one. You expect to sell at least 100 laser printers this month and you need to
make at least $3850 profit on them. How many of what type of p
1. SPECIAL MATH PROJECT
1. Translating Word Problems
2. Integer Problem
3. Age Problem
4. Digit Problem
5. Money Problem
6. Motion Problem
Martinez, Irish Benette M.
Tongo, Faith Bes
Sabino, Hans Ferdinand
Jimenez, Mel Jericho
3. Mr. Fredrickson
asked Russle to buy
him
Red, Blue, and
Green Balloons.
He asked him to buy blue
balloons that is 6 more
than the number of red
balloons.
X + 6
15. 2 years ago, Agnes is 5 years less than the half ofGru’s age and
dave is 7 years younger than agnes, What is dave’s present age
if their ages is equal to 33?
16. Name Age 2 years ago
Gru X X-2
Agnes 1
2
𝑥 - 5
1
2
𝑥 − 5-2
Dave 1
2
𝑥-5-7
1
2
𝑥-5-7-2
26. Let’s try to solve this Digit Word
Problem and analyze it.
27. The digit at the ten’s place of a two digit number is twice
the
digit at the unit’s place. If the sum of this number and the
number formed by reversing the digits is 66. Find the
number.
x2x
28. (2x) (x)
Solution :
Let the unit place digit = x
Ten’s place digit = 2x
TENS UNIT
10 1
Number formed = 10(2x ) + x = 20 x + x = 21x
+
29. (2x) (x)
Solution :
Let the unit place digit = x
Ten’s place digit = 2x
TENS UNIT
10 1
Number formed = 10(2x ) + x = 20 x + x = 21x
+
30. The digit at the ten’s place of a two digit number is twice
the
digit at the unit’s place.
If the sum of this number and the number formed
by reversing the digits is 66. Find the number.
Reversing the digit :
Unit digit = 2x
Ten’s digit = x
1
0
(X) + (2x)1
31. Reversed number formed = 10 (x) + 2x = 10x + 2x = 12x
As the sum of the number is 66.
The equation will be:
21x + 12x = 66
33x = 66
X = 2
Original number formed = 10(2x ) + x = 20 x + x = 21x
32. So unit digit = 2
x = 22x = 10[2(2)]
4 2
The number and the answer is:
33. That’s it! You already know how to solve and analyze Digit
Word Problems. Remember to make your solution neat and
clear so you will not be confused.
34. THANK YOU FOR WATCHING!
“Oh, that’s how!” Rico exclaimed. He was happy because
he learned to solve Digit Word Problems.
36. Sandy wants to have a
lunch with her two friends,
Patrick and Squidward.
37. Sandy is buying 5 krabby patty that cost $ 1.50 each. She
wants to share her burger with her two friends. She asks her
friends to pay for her for their share. Including Patrick, How
much does each person spend on burger?
38. 5 x $1.50 = $7.50
(5 x $1) = $5.00
($0.50 x 5) = $2.50
($5.00 + $2.50) = $7.50
convert $7.50 into cents
750 cents ÷ 3 = 250 cents
250 cents= $2.50
39.
40. A car and another car, who live 14 miles
apart, started at noon to drive towards each
other at the rate of 3 mph and 4 mph
respectively. In how many hours will they
meet?
41. 3X + 4X = 14
7X = 14
7X/7 = 14/7
FIRST DO A TABLE CONSISTING.
THE RATE OR SPEED OF THE
CARS.
THEN MAKE YOUR OWN
WORKING EQUATION.
AFTER THAT COMPUTE FOR THE
FINAL ANSWER, THEN START
CONCLUDING ABOUT YOUR
ANSWER.
RATE TIME DISTANCE
CAR 1 3 X 3X
CAR 2 4 X 4X