Author: Kathy Halverson
Last saved by: Glencoe Mathematics
Company: Halverson Household

Lesson 6-3

Example 1	Solve Proportions

Solve each proportion.
a. 
           = 
     5 ⋅ 36 = 9 ⋅ x	Cross products
        180 = 9x		Multiply.
        =  	Divide each side by 9.
          20 = x

b. 
           = 
 12 ⋅ 15.2 = b ⋅ 4	Cross products
      182.4 = 4b		Multiply.
      = 	Divide each side by 4.
        45.6 = b	

Example 2	Use a Proportions to Solve Problems
MAPS		The scale of a map indicated 1 inch on the map equates to 30 miles of actual distance.  How many miles of actual distance are shown by 4.2 inches on the map?

Explore	You know the actual distance for 1 inch on the map.  You need to find the actual distance for 4.2 inches on the map.

Plan	Write and solve a proportion using ratios that compare map distance to actual distance.  Let d represent the actual distance associated with 4.2 map inches.

Solve	 = 
		       = 			Write a proportion.
		30 ⋅ 4.2 = 1 ⋅ d			Cross products
		      126 = d			Multiply.
	The actual distance related to 4.2 inches on the map is 126 miles.

Check	Check the cross products.  Since 30 ⋅ 4.2 = 126 and 1 ⋅ 126 = 126, the answer is correct.

Real-World EXAMPLE
Example 3	Convert Measurements
PUMPKINS    A large pumpkin has a diameter measuring 29 inches. Find the diameter of the pumpkin in centimeters if 1 in. = 2.54 cm. 
Let x represent the diameter in centimeters.
    
	        		      1 ⋅ x = 2.54 ⋅ 29		Cross products
	            	           x = 73.66		Simplify.
The diameter of the pumpkin is 73.66 centimeters.