Math Practice Online > free > lessons > Arizona > 8th grade > Algebraic Word Problems

These sample problems below for Algebraic Word Problems were generated by the MathScore.com engine.

## Sample Problems For Algebraic Word Problems

### Complexity=5, Mode=1

Answer these word problems.
 1 You collect coins. At your request, Michelle decides to triple your quantity of coins. In the end, you have 48 coins. How many coins did you originally have? 2 You collect coins. Since you're cool, you give Steve 4 coins. In the end, you have 11 coins. How many coins did you originally have?

### Complexity=8, Mode=2

Answer these word problems.
 1 You collect marbles. Catherine takes half of your marbles. At your request, Sarah decides to triple your quantity of marbles. In the end, you have 33 marbles. How many marbles did you originally have? 2 You collect marbles. At your request, Emily decides to double your quantity of marbles. At your request, Jack decides to double your quantity of marbles. In the end, you have 40 marbles. How many marbles did you originally have?

### Complexity=10, Mode=3

Answer these word problems.
 1 You collect baseball cards. Catherine gives you another 16 baseball cards. Since you're cool, you give John 34 baseball cards. Isabel gives you another 16 baseball cards. In the end, you have 20 baseball cards. How many baseball cards did you originally have? 2 You collect balls. Since you're cool, you give Bob 10 balls. Jeff gives you another 10 balls. At your request, Christine decides to quadruple your quantity of balls. In the end, you have 96 balls. How many balls did you originally have?

### Complexity=20, Mode=4

Answer these word problems.
 1 You collect coins. Daphne takes half of one more than the number of coins you have. Jane takes half of one less than the number of coins you have. At your request, Catherine decides to triple your quantity of coins. Patricia takes half of one less than the number of coins you have. In the end, you have 8 coins. How many coins did you originally have? 2 You collect baseball cards. Mary gives you another 15 baseball cards. At your request, Sam decides to double your quantity of baseball cards. Emily takes half of your baseball cards. Since you're cool, you give Sarah 12 baseball cards. In the end, you have 22 baseball cards. How many baseball cards did you originally have?

### Complexity=5, Mode=1

Answer these word problems.
1You collect coins. At your request, Michelle decides to triple your quantity of coins. In the end, you have 48 coins. How many coins did you originally have?
Solution
Michelle triples the number of coins you have: x × 3.
So we solve: x × 3 = 48 coins.
x = 16 coins.
2You collect coins. Since you're cool, you give Steve 4 coins. In the end, you have 11 coins. How many coins did you originally have?
Solution
Steve takes 4 coins from you: x - 4.
So we solve: x - 4 = 11 coins.
x = 15 coins.

### Complexity=8, Mode=2

Answer these word problems.
1You collect marbles. Catherine takes half of your marbles. At your request, Sarah decides to triple your quantity of marbles. In the end, you have 33 marbles. How many marbles did you originally have?
Solution
Catherine takes half of the number of marbles you have: x ÷ 2.
Sarah triples the number of marbles you have: (x ÷ 2) × 3.
So we solve: (x ÷ 2) × 3 = 33 marbles.
x ÷ 2 = 11 marbles.
x = 22 marbles.
2You collect marbles. At your request, Emily decides to double your quantity of marbles. At your request, Jack decides to double your quantity of marbles. In the end, you have 40 marbles. How many marbles did you originally have?
Solution
Emily doubles the number of marbles you have: x × 2.
Jack doubles the number of marbles you have: (x × 2) × 2.
So we solve: (x × 2) × 2 = 40 marbles.
x × 2 = 20 marbles.
x = 10 marbles.

### Complexity=10, Mode=3

Answer these word problems.
1You collect baseball cards. Catherine gives you another 16 baseball cards. Since you're cool, you give John 34 baseball cards. Isabel gives you another 16 baseball cards. In the end, you have 20 baseball cards. How many baseball cards did you originally have?
Solution
Suppose you start with x baseball cards.
Catherine gives you 16 baseball cards: x + 16.
John takes 34 baseball cards from you: (x + 16) - 34.
Isabel gives you 16 baseball cards: ((x + 16) - 34) + 16.
So we solve: ((x + 16) - 34) + 16 = 20 baseball cards.
(x + 16) - 34 = 4 baseball cards.
x + 16 = 38 baseball cards.
x = 22 baseball cards.
2You collect balls. Since you're cool, you give Bob 10 balls. Jeff gives you another 10 balls. At your request, Christine decides to quadruple your quantity of balls. In the end, you have 96 balls. How many balls did you originally have?
Solution
Bob takes 10 balls from you: x - 10.
Jeff gives you 10 balls: (x - 10) + 10.
Christine quadruples the number of balls you have: ((x - 10) + 10) × 4.
So we solve: ((x - 10) + 10) × 4 = 96 balls.
(x - 10) + 10 = 24 balls.
x - 10 = 14 balls.
x = 24 balls.

### Complexity=20, Mode=4

Answer these word problems.
1You collect coins. Daphne takes half of one more than the number of coins you have. Jane takes half of one less than the number of coins you have. At your request, Catherine decides to triple your quantity of coins. Patricia takes half of one less than the number of coins you have. In the end, you have 8 coins. How many coins did you originally have?
Solution
Daphne takes half of one more than the number of coins you have. This is the same as leaving you half of one less than the number of coins you have: (x - 1) ÷ 2.
Jane takes half of one less than the number of coins you have. This is the same as leaving you half of one more than the number of coins you have: (((x - 1) ÷ 2) + 1) ÷ 2.
Catherine triples the number of coins you have: ((((x - 1) ÷ 2) + 1) ÷ 2) × 3.
Patricia takes half of one less than the number of coins you have. This is the same as leaving you half of one more than the number of coins you have: ((((((x - 1) ÷ 2) + 1) ÷ 2) × 3) + 1) ÷ 2.
So we solve: ((((((x - 1) ÷ 2) + 1) ÷ 2) × 3) + 1) ÷ 2 = 8 coins.
((((x - 1) ÷ 2) + 1) ÷ 2) × 3 = 15 coins.
(((x - 1) ÷ 2) + 1) ÷ 2 = 5 coins.
(x - 1) ÷ 2 = 9 coins.
x = 19 coins.
2You collect baseball cards. Mary gives you another 15 baseball cards. At your request, Sam decides to double your quantity of baseball cards. Emily takes half of your baseball cards. Since you're cool, you give Sarah 12 baseball cards. In the end, you have 22 baseball cards. How many baseball cards did you originally have?
Solution
Suppose you start with x baseball cards.
Mary gives you 15 baseball cards: x + 15.
Sam doubles the number of baseball cards you have: (x + 15) × 2.
Emily takes half of the number of baseball cards you have: ((x + 15) × 2) ÷ 2.
Sarah takes 12 baseball cards from you: (((x + 15) × 2) ÷ 2) - 12.
So we solve: (((x + 15) × 2) ÷ 2) - 12 = 22 baseball cards.
((x + 15) × 2) ÷ 2 = 34 baseball cards.
(x + 15) × 2 = 68 baseball cards.
x + 15 = 34 baseball cards.
x = 19 baseball cards.

MathScore.com

Copyright Accurate Learning Systems Corporation 2008.
MathScore is a registered trademark.