Page 180 - ABCTE Study Guide_Neat

Since cross products must be equal in a proportion, you can use this property to solve for a missing piece
of information in a proportion.

Step 1. Cross multiply.

Step 2. Use division to solve for the variable.

Let's look at another proportion:

In this example, you can make equivalent fractions by determining what 5 is multiplied by to get 30.
Because it is 6, you would also have to multiply 8 by 6, obtaining 48. Although this works in this example,
when the answers are not integers, using cross multiplication is more efficient and accurate.

Solving More Complex Proportions

The method for solving proportions is always the same: cross multiply and isolate the variable. But it may
take more than two steps to get the variable alone, as in the following examples.

Solve

Cross multiply: 20(x+4) = 90

Distributive Property: 20x + 80 = 90

Subtract 80 from both sides: 20x = 10

Divide both sides by 20:

Question

The ratio of women to men at a party is 4 : 3. If there are 120 men at the party, how many women are
there?

A 90

B 150

C 160