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ALGEBRAIC EQUATIONS

Writing Algebraic Equations

Problem: Jeanne has $17 in her piggy bank. How much money does she need to buy a game that costs $68?

Solution: Let x represent the amount of money Jeanne needs. Then the following equation can represent this problem:

17 + x = 68

We can subtract 17 from both sides of the equation to find the value of x.

68 - 17 = x

Answer: x = 51, so Jeanne needs $51 to buy the game.

In the problem above, x is a variable. The symbols 17 + x = 68 form an algebraic equation. Let’s look at some examples of writing algebraic equations.

Example 1: Write each sentence as an algebraic equation

Sentence

A number increased by nine is fifteen.

Twice a number is eighteen.

Four less than a number is twenty.

A number divided by six is eight.

Algebraic Equation

y + 9 = 15

2n = 18

x - 4 = 20

k

6

= 8

Example 2: Write each sentence as an algebraic equation.

Sentence

Twice a number, decreased by twenty-nine, is seven.

Thirty-two is twice a number increased by eight.

The quotient of fifty and five more than a number is ten.

Twelve is sixteen less than four times a number.

Algebraic Equation

2t - 29 = 7

32 = 2a + 8

50

n + 5

= 10

12 = 4x - 16

Example 3: Write each sentence as an algebraic equation

Sentence

Eleni is x years old. In thirteen years she will be twenty-four years old.

Each piece of candy costs 25 cents. The price of h pieces of candy is $2.00.

Suzanne made a withdrawal of d dollars from her savings account. Her old balance was $350,

and her new balance is $280.

A large pizza pie with 15 slices is shared among p students so that each student’s

share is 3 slices.

Algebraic Equation

x + 13 = 24

25h = 200

350 - d = 280

15

p

= 3