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Algebraic Word Problems - Sample Math Practice Problems

The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically graded and the difficulty adapts dynamically based on performance. Answers to these sample questions appear at the bottom of the page. This page does not grade your responses.

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Complexity=1, Mode=alg

Answer these word problems.

1.  
You collect sand dollars. Since you're nice, you give Tiffany 15 sand dollars. At the end you have 3. How many sand dollars did you start with?
2.  
You collect balls. Since her mother makes balls, Cindy decides to triple your balls. At the end you have 54. How many balls did you start with?

Complexity=2, Mode=alg

Answer these word problems.

1.  
You collect marbles. Mary takes half of one less than the number of marbles you have. At the end you have 7. How many marbles did you start with?
2.  
You collect balls. Since his father makes balls, Steven decides to double your balls. Paul gives you another 5 balls. At the end you have 31. How many balls did you start with?

Complexity=3, Mode=alg

Answer these word problems.

1.  
You collect sand dollars. Tiffany gives you another 21 sand dollars. Jennifer gives you another 8 sand dollars. Since you're nice, you give Pearl 19 sand dollars. At the end you have 28. How many sand dollars did you start with?
2.  
You collect sand dollars. Since you're nice, you give Mary 7 sand dollars. Miguel gives you another 7 sand dollars. Since you're nice, you give Peter 11 sand dollars. At the end you have 7. How many sand dollars did you start with?

Complexity=4, Mode=alg

Answer these word problems.

1.  
You collect baseball cards. John takes half of one less than the number of baseball cards you have. Since you're nice, you give Peter 1 baseball card. Since her father makes baseball cards, Mary decides to quadruple your baseball cards. At the end you have 28. How many baseball cards did you start with?
2.  
You collect baseball cards. Since you're nice, you give Jennifer 2 baseball cards. Since his mother makes baseball cards, Miguel decides to quadruple your baseball cards. Jose gives you another 7 baseball cards. Cindy gives you another 5 baseball cards. At the end you have 64. How many baseball cards did you start with?

Complexity=5, Mode=alg

Answer these word problems.

1.  
You collect pencils. Since his father makes pencils, John decides to quadruple your pencils. Pearl gives you another 8 pencils. Miguel gives you another 22 pencils. Since you're nice, you give Sharon 80 pencils. Jose gives you another 10 pencils. At the end you have 60. How many pencils did you start with?
2.  
You collect sand dollars. Since her mother collects sand dollars, Cindy decides to triple your sand dollars. Since her father collects sand dollars, Maria decides to double your sand dollars. Jennifer takes half of your sand dollars. Since her mother collects sand dollars, Tiffany decides to double your sand dollars. Mary gives you another 25 sand dollars. At the end you have 175. How many sand dollars did you start with?

Answers

Complexity=1, Mode=alg

Answer these word problems.

#ProblemCorrect AnswerYour Answer
1You collect sand dollars. Since you're nice, you give Tiffany 15 sand dollars. At the end you have 3. How many sand dollars did you start with?
Solution
Suppose you start with x sand dollars.
Tiffany takes 15 sand dollars from you. Now you have x - 15.
So we solve this equation for x:
x - 15 = 3
x = 18
You can double check your answer by plugging 18 into x in the original equation or seeing whether it fits the description.
#ProblemCorrect AnswerYour Answer
2You collect balls. Since her mother makes balls, Cindy decides to triple your balls. At the end you have 54. How many balls did you start with?
Solution
Suppose you start with x balls.
Cindy triples the number of balls you have. Now you have x × 3.
So we solve this equation for x:
x × 3 = 54
x = 18
You can double check your answer by plugging 18 into x in the original equation or seeing whether it fits the description.

Complexity=2, Mode=alg

Answer these word problems.

#ProblemCorrect AnswerYour Answer
1You collect marbles. Mary takes half of one less than the number of marbles you have. At the end you have 7. How many marbles did you start with?
Solution
Suppose you start with x marbles.
Mary takes half of one less than the number of marbles you have. This can only happen when you start with an odd number, and Mary takes one less than they leave you. So you should be left with half of one more:
(x + 1) ÷ 2.
So we solve this equation for x:
(x + 1) ÷ 2 = 7
x + 1 = 14
x = 13
You can double check your answer by plugging 13 into x in the original equation or seeing whether it fits the description.
#ProblemCorrect AnswerYour Answer
2You collect balls. Since his father makes balls, Steven decides to double your balls. Paul gives you another 5 balls. At the end you have 31. How many balls did you start with?
Solution
Suppose you start with x balls.
Steven doubles the number of balls you have. Now you have x × 2.
Paul gives you 5 balls. Now you have (x × 2) + 5.
So we solve this equation for x:
(x × 2) + 5 = 31
x × 2 = 26
x = 13
You can double check your answer by plugging 13 into x in the original equation or seeing whether it fits the description.

Complexity=3, Mode=alg

Answer these word problems.

#ProblemCorrect AnswerYour Answer
1You collect sand dollars. Tiffany gives you another 21 sand dollars. Jennifer gives you another 8 sand dollars. Since you're nice, you give Pearl 19 sand dollars. At the end you have 28. How many sand dollars did you start with?
Solution
Suppose you start with x sand dollars.
Tiffany gives you 21 sand dollars. Now you have x + 21.
Jennifer gives you 8 sand dollars. Now you have (x + 21) + 8.
Pearl takes 19 sand dollars from you. Now you have ((x + 21) + 8) - 19.
So we solve this equation for x:
((x + 21) + 8) - 19 = 28
(x + 21) + 8 = 47
x + 21 = 39
x = 18
You can double check your answer by plugging 18 into x in the original equation or seeing whether it fits the description.
#ProblemCorrect AnswerYour Answer
2You collect sand dollars. Since you're nice, you give Mary 7 sand dollars. Miguel gives you another 7 sand dollars. Since you're nice, you give Peter 11 sand dollars. At the end you have 7. How many sand dollars did you start with?
Solution
Suppose you start with x sand dollars.
Mary takes 7 sand dollars from you. Now you have x - 7.
Miguel gives you 7 sand dollars. Now you have (x - 7) + 7.
Peter takes 11 sand dollars from you. Now you have ((x - 7) + 7) - 11.
So we solve this equation for x:
((x - 7) + 7) - 11 = 7
(x - 7) + 7 = 18
x - 7 = 11
x = 18
You can double check your answer by plugging 18 into x in the original equation or seeing whether it fits the description.

Complexity=4, Mode=alg

Answer these word problems.

#ProblemCorrect AnswerYour Answer
1You collect baseball cards. John takes half of one less than the number of baseball cards you have. Since you're nice, you give Peter 1 baseball card. Since her father makes baseball cards, Mary decides to quadruple your baseball cards. At the end you have 28. How many baseball cards did you start with?
Solution
Suppose you start with x baseball cards.
John takes half of one less than the number of baseball cards you have. This can only happen when you start with an odd number, and John takes one less than they leave you. So you should be left with half of one more:
(x + 1) ÷ 2.
Peter takes 1 baseball card from you. Now you have ((x + 1) ÷ 2) - 1.
Mary quadruples the number of baseball cards you have. Now you have (((x + 1) ÷ 2) - 1) × 4.
So we solve this equation for x:
(((x + 1) ÷ 2) - 1) × 4 = 28
((x + 1) ÷ 2) - 1 = 7
(x + 1) ÷ 2 = 8
x + 1 = 16
x = 15
You can double check your answer by plugging 15 into x in the original equation or seeing whether it fits the description.
#ProblemCorrect AnswerYour Answer
2You collect baseball cards. Since you're nice, you give Jennifer 2 baseball cards. Since his mother makes baseball cards, Miguel decides to quadruple your baseball cards. Jose gives you another 7 baseball cards. Cindy gives you another 5 baseball cards. At the end you have 64. How many baseball cards did you start with?
Solution
Suppose you start with x baseball cards.
Jennifer takes 2 baseball cards from you. Now you have x - 2.
Miguel quadruples the number of baseball cards you have. Now you have (x - 2) × 4.
Jose gives you 7 baseball cards. Now you have ((x - 2) × 4) + 7.
Cindy gives you 5 baseball cards. Now you have (((x - 2) × 4) + 7) + 5.
So we solve this equation for x:
(((x - 2) × 4) + 7) + 5 = 64
((x - 2) × 4) + 7 = 59
(x - 2) × 4 = 52
x - 2 = 13
x = 15
You can double check your answer by plugging 15 into x in the original equation or seeing whether it fits the description.

Complexity=5, Mode=alg

Answer these word problems.

#ProblemCorrect AnswerYour Answer
1You collect pencils. Since his father makes pencils, John decides to quadruple your pencils. Pearl gives you another 8 pencils. Miguel gives you another 22 pencils. Since you're nice, you give Sharon 80 pencils. Jose gives you another 10 pencils. At the end you have 60. How many pencils did you start with?
Solution
Suppose you start with x pencils.
John quadruples the number of pencils you have. Now you have x × 4.
Pearl gives you 8 pencils. Now you have (x × 4) + 8.
Miguel gives you 22 pencils. Now you have ((x × 4) + 8) + 22.
Sharon takes 80 pencils from you. Now you have (((x × 4) + 8) + 22) - 80.
Jose gives you 10 pencils. Now you have ((((x × 4) + 8) + 22) - 80) + 10.
So we solve this equation for x:
((((x × 4) + 8) + 22) - 80) + 10 = 60
(((x × 4) + 8) + 22) - 80 = 50
((x × 4) + 8) + 22 = 130
(x × 4) + 8 = 108
x × 4 = 100
x = 25
You can double check your answer by plugging 25 into x in the original equation or seeing whether it fits the description.
#ProblemCorrect AnswerYour Answer
2You collect sand dollars. Since her mother collects sand dollars, Cindy decides to triple your sand dollars. Since her father collects sand dollars, Maria decides to double your sand dollars. Jennifer takes half of your sand dollars. Since her mother collects sand dollars, Tiffany decides to double your sand dollars. Mary gives you another 25 sand dollars. At the end you have 175. How many sand dollars did you start with?
Solution
Suppose you start with x sand dollars.
Cindy triples the number of sand dollars you have. Now you have x × 3.
Maria doubles the number of sand dollars you have. Now you have (x × 3) × 2.
Jennifer takes half of the number of sand dollars you have: ((x × 3) × 2) ÷ 2.
Tiffany doubles the number of sand dollars you have. Now you have (((x × 3) × 2) ÷ 2) × 2.
Mary gives you 25 sand dollars. Now you have ((((x × 3) × 2) ÷ 2) × 2) + 25.
So we solve this equation for x:
((((x × 3) × 2) ÷ 2) × 2) + 25 = 175
(((x × 3) × 2) ÷ 2) × 2 = 150
((x × 3) × 2) ÷ 2 = 75
(x × 3) × 2 = 150
x × 3 = 75
x = 25
You can double check your answer by plugging 25 into x in the original equation or seeing whether it fits the description.
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