Math Practice Problems - Algebraic Word Problems

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=5, Mode=1

Answer these word problems.

1.	You collect stamps. Jose gives you another 24 stamps. In the end, you have 46 stamps. How many stamps did you originally have?
2.	You collect baseball cards. Since you're cool, you give Alice 9 baseball cards. In the end, you have 2 baseball cards. How many baseball cards did you originally have?

Complexity=8, Mode=2

Answer these word problems.

1.	You collect balls. Liz takes half of one less than the number of balls you have. Since you're cool, you give Isabel 2 balls. In the end, you have 10 balls. How many balls did you originally have?
2.	You collect stamps. Jose takes half of one less than the number of stamps you have. At your request, Liz decides to double your quantity of stamps. In the end, you have 6 stamps. How many stamps did you originally have?

Complexity=10, Mode=3

Answer these word problems.

1.	You collect stamps. Jeff gives you another 12 stamps. Since you're cool, you give Christine 10 stamps. Jeff takes half of your stamps. In the end, you have 8 stamps. How many stamps did you originally have?
2.	You collect jelly beans. Since you're cool, you give Sarah 22 jelly beans. Lisa gives you another 23 jelly beans. Michelle gives you another 20 jelly beans. In the end, you have 44 jelly beans. How many jelly beans did you originally have?

Complexity=20, Mode=4

Answer these word problems.

1.	You collect dollars. Emily gives you another 19 dollars. Since you're cool, you give Jack 4 dollars. George takes half of your dollars. Jose takes half of one more than the number of dollars you have. In the end, you have 9 dollars. How many dollars did you originally have?
2.	You collect baseball cards. Since you're cool, you give Steve 1 baseball card. Since you're cool, you give Dennis 4 baseball cards. Sam gives you another 23 baseball cards. At your request, John decides to quadruple your quantity of baseball cards. In the end, you have 100 baseball cards. How many baseball cards did you originally have?

Answers

Complexity=5, Mode=1

Answer these word problems.

#	Problem	Correct Answer	Your Answer
1	You collect stamps. Jose gives you another 24 stamps. In the end, you have 46 stamps. How many stamps did you originally have?
Solution Suppose you start with x stamps. Jose gives you 24 stamps: x + 24. So we solve: x + 24 = 46 stamps. x = 22 stamps.

#	Problem	Correct Answer	Your Answer
2	You collect baseball cards. Since you're cool, you give Alice 9 baseball cards. In the end, you have 2 baseball cards. How many baseball cards did you originally have?
Solution Suppose you start with x baseball cards. Alice takes 9 baseball cards from you: x - 9. So we solve: x - 9 = 2 baseball cards. x = 11 baseball cards.

Complexity=8, Mode=2

Answer these word problems.

#	Problem	Correct Answer	Your Answer
1	You collect balls. Liz takes half of one less than the number of balls you have. Since you're cool, you give Isabel 2 balls. In the end, you have 10 balls. How many balls did you originally have?
Solution Suppose you start with x balls. Liz takes half of one less than the number of balls you have. This is the same as leaving you half of one more than the number of balls you have: (x + 1) ÷ 2. Isabel takes 2 balls from you: ((x + 1) ÷ 2) - 2. So we solve: ((x + 1) ÷ 2) - 2 = 10 balls. (x + 1) ÷ 2 = 12 balls. x = 23 balls.

#	Problem	Correct Answer	Your Answer
2	You collect stamps. Jose takes half of one less than the number of stamps you have. At your request, Liz decides to double your quantity of stamps. In the end, you have 6 stamps. How many stamps did you originally have?
Solution Suppose you start with x stamps. Jose takes half of one less than the number of stamps you have. This is the same as leaving you half of one more than the number of stamps you have: (x + 1) ÷ 2. Liz doubles the number of stamps you have: ((x + 1) ÷ 2) × 2. So we solve: ((x + 1) ÷ 2) × 2 = 6 stamps. (x + 1) ÷ 2 = 3 stamps. x = 5 stamps.

Complexity=10, Mode=3

Answer these word problems.

#	Problem	Correct Answer	Your Answer
1	You collect stamps. Jeff gives you another 12 stamps. Since you're cool, you give Christine 10 stamps. Jeff takes half of your stamps. In the end, you have 8 stamps. How many stamps did you originally have?
Solution Suppose you start with x stamps. Jeff gives you 12 stamps: x + 12. Christine takes 10 stamps from you: (x + 12) - 10. Jeff takes half of the number of stamps you have: ((x + 12) - 10) ÷ 2. So we solve: ((x + 12) - 10) ÷ 2 = 8 stamps. (x + 12) - 10 = 16 stamps. x + 12 = 26 stamps. x = 14 stamps.

#	Problem	Correct Answer	Your Answer
2	You collect jelly beans. Since you're cool, you give Sarah 22 jelly beans. Lisa gives you another 23 jelly beans. Michelle gives you another 20 jelly beans. In the end, you have 44 jelly beans. How many jelly beans did you originally have?
Solution Suppose you start with x jelly beans. Sarah takes 22 jelly beans from you: x - 22. Lisa gives you 23 jelly beans: (x - 22) + 23. Michelle gives you 20 jelly beans: ((x - 22) + 23) + 20. So we solve: ((x - 22) + 23) + 20 = 44 jelly beans. (x - 22) + 23 = 24 jelly beans. x - 22 = 1 jelly bean. x = 23 jelly beans.

Complexity=20, Mode=4

Answer these word problems.

#	Problem	Correct Answer	Your Answer
1	You collect dollars. Emily gives you another 19 dollars. Since you're cool, you give Jack 4 dollars. George takes half of your dollars. Jose takes half of one more than the number of dollars you have. In the end, you have 9 dollars. How many dollars did you originally have?
Solution Suppose you start with x dollars. Emily gives you 19 dollars: x + 19. Jack takes 4 dollars from you: (x + 19) - 4. George takes half of the number of dollars you have: ((x + 19) - 4) ÷ 2. Jose takes half of one more than the number of dollars you have. This is the same as leaving you half of one less than the number of dollars you have: ((((x + 19) - 4) ÷ 2) - 1) ÷ 2. So we solve: ((((x + 19) - 4) ÷ 2) - 1) ÷ 2 = 9 dollars. ((x + 19) - 4) ÷ 2 = 19 dollars. (x + 19) - 4 = 38 dollars. x + 19 = 42 dollars. x = 23 dollars.

#	Problem	Correct Answer	Your Answer
2	You collect baseball cards. Since you're cool, you give Steve 1 baseball card. Since you're cool, you give Dennis 4 baseball cards. Sam gives you another 23 baseball cards. At your request, John decides to quadruple your quantity of baseball cards. In the end, you have 100 baseball cards. How many baseball cards did you originally have?
Solution Suppose you start with x baseball cards. Steve takes 1 baseball card from you: x - 1. Dennis takes 4 baseball cards from you: (x - 1) - 4. Sam gives you 23 baseball cards: ((x - 1) - 4) + 23. John quadruples the number of baseball cards you have: (((x - 1) - 4) + 23) × 4. So we solve: (((x - 1) - 4) + 23) × 4 = 100 baseball cards. ((x - 1) - 4) + 23 = 25 baseball cards. (x - 1) - 4 = 2 baseball cards. x - 1 = 6 baseball cards. x = 7 baseball cards.

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