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Algebraic Word Problems

To do well in this topic, you will need to know how to do arithmetic word problems first.
To review arithmetic word problems, see here.

Algebraic word problems are word problems that involve solving for an unknown.

Example 1: Addition and Subtraction

Answer these word problems
You collect jelly beans. Steve gives you another 15 jelly beans. Since you're cool, you give Sam 9 jelly beans. In the end, you have 31 jelly beans. How many jelly beans did you originally have?

The unknown is the number of jelly beans you started with, so assign a variable to the unknown.
Then translate the word problem into an equation and solve.

 Let x = number of jelly beans you started with. 1. You start out with x jelly beans x 2. Steve gives you 15 jelly beans x + 15 3. You give Sam 9 jelly beans x + 15 - 9 4. In the end, you have 31 jelly beans x + 15 - 9 = 31 Solve the equation for x x + 15 - 9 = 31 x + 6 = 31 x + 6 - 6 = 31 - 6 x = 25
x = number of jelly beans you started with = 25 jelly beans.
How many jelly beans did you originally have?

Example 2: Multiplication and Division

Answer these word problems
You collect baseball cards. At your request, Patricia decides to triple your quantity of baseball cards. Catherine takes half of your baseball cards. In the end, you have 12 baseball cards. How many baseball cards did you originally have?

The unknown is the number of baseball cards you started with, so assign a variable to the unknown.
Then translate the word problem into an equation and solve.

 Let n = number of baseball cards you started with. 1. You start out with n baseball cards n 2. Patricia triples your baseball cards n × 3 3. Catherine takes half your baseball cards n × 3 ÷ 2 4. In the end, you have 12 baseball cards n × 3 ÷ 2 = 12 Solve the equation for n n × 3 ÷ 2 = 12 n × 3 ÷ 2 × 2 = 12 × 2 n × 3 = 24 n × 3 ÷ 3 = 24 ÷ 3 n = 8
n = number of baseball cards you started with = 8 baseball cards.
How many baseball cards did you originally have?

Example 3: Addition, Subtraction, and Division

Answer these word problems
You collect baseballs. Justin gives you 14 baseballs. Jane takes half of your baseballs. Since you're cool, you give Bob 3 baseballs. In the end, you have 6 baseballs. How many baseballs did you originally have?

The unknown is the number of baseballs you started with, so assign a variable to the unknown.
Then translate the word problem into an equation and solve.

 Let b = number of baseballs you started with. 1. You start out with b baseballs b 2. Justin gives you 14 baseballs b + 14 3. Jane takes half of your baseballs (b + 14) ÷ 2 4. You give Bob 3 baseballs (b + 14) ÷ 2 - 3 5. In the end, you have 6 baseballs (b + 14) ÷ 2 - 3 = 6 Solve the equation for b. (b + 14) ÷ 2 - 3 = 6 (b + 14) ÷ 2 - 3 + 3 = 6 + 3 (b + 14) ÷ 2 = 9 (b + 14) ÷ 2 × 2 = 9 × 2 b + 14 = 18 b + 14 - 14 = 18 - 14 b = 4
b = number of baseballs you started with = 4 baseballs.
How many baseballs did you originally have?

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