Learning Target: I can calculate the base of a percentage in an equation.

Example

Find n.  48% of n = 24.

Solve by Using an Equation

Step 1: Write an equation.

48% of n means that n is being multiplied by 0.48.

Think -- "of" means "times"

0.48  ×  n = 24

 

Step 2: Solve for n.

 n is being multiplied by a number in the equation.

Perform the inverse operation to get n alone --

Divide both sides by 0.48

 

n = 50

Solve by Setting Up a Proportion

Step 1: Write a proportion for 48% of n = 24.

This means that 48 parts of 100 is equal to 24 parts of n.

 

 

 

Step 2: Use cross multiplication to solve for n.

24  ×  100 = n  ×  48

2,400 = 48n

50 = n

In the equation 48% of n = 24, n = 50.

Let's Practice Together

Find each number.

1.)    180 is 30% of what number?

2.)   21 is 42% of what number? 

Your Turn

Use a proportion to find each number.

3.)   70 is 25% of what number?

4.)   45% of what number is 4.5?

5.)   10 is 20% of what number?

6.)   10% of what number is 111?

Use an equation to find each number.

8.)   25% of what number is 22?

9.)   35% of what number is 7?

10.)   8% of what number is 16?

Check for Understanding

1.)  A local book fair is selling 72 young adult novels.  If 15% of the available books are young adult novels, how many books are in the fair altogether?

2.)  Dave deposits 20% of his paycheck into his savings account every week.  If his last deposit in the account was $75, how much was his paycheck that week?

Answers

1.  600

2.  50

3.  280

4.  10

5.  50

6.  1110

7.  290

8.  88

9.  20

10.  200

Check for Understanding

1.  480

2.  $375