SECTION 2.6 Ratio, Proportion, and Percent^133
Solving an Equation by Using Cross ProductsSolve the equation
Cross products
Distributive property
Add 6.
Subtract 5m.Divide by.The solution set isE- (^112) F. NOW TRY
m=- - 2
11
2
- 2 m= 11
3 m= 5 m+ 11
3 m- 6 = 5 m+ 5
31 m- 22 = 51 m+ 12
m- 2
5
=
m+ 1
3
m- 25 =
m+ 13.
EXAMPLE 5
Be sure to use
parentheses.NOTE When you set cross products equal to each other, you are really multiplying
each ratio in the proportion by a common denominator.
OBJECTIVE 3 Solve applied problems by using proportions.
Applying ProportionsAfter Lee Ann Spahr had pumped 5.0 gal of gasoline, the display showing the price
read $16.60. When she finished pumping the gasoline, the price display read $48.14.
How many gallons did she pump?
To solve this problem, set up a proportion, with prices in the numerators and
gallons in the denominators. Let the number of gallons she pumped.
Cross products
Multiply.
Divide by 16.60.She pumped 14.5 gal. Check this answer. (Using a calculator reduces the possibility
of error.) Notice that the way the proportion was set up uses the fact that the unit price
is the same, no matter how many gallons are purchased. NOW TRY
x= 14.5
16.60x= 240.70
16.60x= 5.0 1 48.14 2
$16.60
5.0
=
$48.14
x
x=
NOW TRY EXAMPLE 6
EXERCISE 6
Twenty gallons of gasoline
costs $49.80. How much
would 27 gal of the same
gasoline cost?
Price Price
Gallons Gallons
Be sure that numerators represent
the samequantities and denomina-
tors represent the samequantities.OBJECTIVE 4 Find percents and percentages. A percent is a ratio where the
second number is always 100.For example,
50% represents the ratio of 50 to 100, that is, , or, as a decimal, 0.50.
27%represents the ratio of 27 to 100, that is, , or, as a decimal, 0.27.
Since the word percentmeans “per 100,”one percent means “one per one hundred.”
or 1%
1
100
1%0.01,
27
10050
100NOW TRY
EXERCISE 5
Solve the equation.
k- 3
6=
3 k+ 2
4NOW TRY ANSWERS
- E-^127 F 6.$67.23