Basic Mathematics for College Students

We have found that the unknown term in the proportion is 6 and we can write:

To check this result, we find the cross products.

Check:

Since the cross products are equal, the result, 6, checks.
In the previous example, when we find the value of the variable xthat makes the
given proportion true, we say that we have solved the proportionto find the unknown
term.

The Language of Mathematics We solve proportions by writing a series of

steps that result in an equation of the form xa numberor a numberx.We

say that the variable xis isolatedon one side of the equation.Isolatedmeans

alone or by itself.

Solving a Proportion to Find an Unknown Term

1. Set the cross products equal to each other to form an equation.


2. Isolate the variable on one side of the equation by dividing both sides by the
   number that is multiplied by that variable.


3. Check by substituting the result into the original proportion and finding the
   cross products.

5  24  120

6 20  6  120

5

^24

20

6

5



24

20

5.2 Proportions 433

EXAMPLE 6

Solve the proportion:

StrategyWe will set the cross products equal to each other to form an equation.

WHYThen we can isolate the variable xon one side of the equation to find the
unknown term that it represents.

Solution

This is the proportion to solve.

Set the cross products equal to each other to form an equation.

To simplify the right side of the equation, multiply: 20  3 60.

To simplify the left side, remove the common factor of 12.

To simplify the right side of the equation, do the division: 60  12 5.

Thus,xis 5. To check this result, we substitute 5 for xin the original proportion.

Check:

Since the cross products are equal, the result, 5, checks.

20  3  60

12 5  12  60

20

^3

5

x 5

To undo the multiplication by 12 and

(^) isolate x, divide both sides by 12.
12 x
12



60

12

12 x 60

12 x 20  3

12

20



3

x

12

20



3

x

Self Check 6

Solve the proportion:

Now TryProblem 41

15

x



20

32

5

12  60

 60

0