Writing Equations

Turning Words into Equations Similar to turning words into expressionsThe word is tells you where your equal sign goes

Write each sentence as an algebraic equation:

A number increased by 9 is 15

n + 9 = 15

Twice a number is 18

2n = 18

Four less than a number is 20

n – 4 = 20

A number divided by 6 is 8

n/6 = 8

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

2a – 29 = 7

Thirty-two is twice a number decreased by eight

32 = 2b - 8

Twelve is sixteen less than four times a number

12 = 4p - 16

Writing Equations for Word Problems

Example:

Bhavin’s age 7 years from now will be 20.We don’t know Bhavin’s current ageWe do know in 7 years she will be 20

We should pick a variable to represent the unknown value. In this case, it’s Bhavin’s age. Let’s let a represent Bhavin’s age

So, the equation to figure out Bhavin’s age will be:

a+7 = 20

We use equations to solve for the unknown or variable. This means, we want to figure out what the variable is.

Bhavin’s age 7 years from now will be 20. So, how old is she now?

Let a represent how old she is now

a + 7 = 20

a + 7 – 7 = 20 – 7

a = 13

Solution: Bhavin’s current age is 13

How could we CHECK to see if our solution is right?

Look back:

Let a represent how old she is now

a + 7 = 20

a + 7 – 7 = 20 – 7

a = 13

Solution: Bhavin’s current age is 13

Check:

When a= 13, a +7 = 20

LS RS

a + 7 20

= (13) + 7

= 20

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

x + 13 = 24

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

.25h = 2.00

Suzanne made a withdrawal of d dollars from her savings account. Her old balance was $350, and her new balance is $280.

350 – d = 280

A large pizza pie with 15 slices is shared among a group of p students so that each student’s share is 3 slices.

15/p = 3