SECTION 2.6 Ratio, Proportion, and Percent^131
To find the best buy, write ratios comparing the price for each size of jar to the
number of units (ounces) per jar. Then divide to obtain the price per unit (ounce).
Size Unit Cost (dollars per ounce)18 oz The best buy28 oz40 oz $3.98
40
=$0.100$2.97
28 =$0.106$1.78
18 =$0.099
(Results are rounded to
the nearest thousandth.)Because the 18-oz size produces the lowest unit cost, it is the best buy. This
example shows that buying the largest size does not always provide the best buy.
NOW TRYOBJECTIVE 2 Solve proportions.A ratio is used to compare two numbers or
amounts. A proportionsays that two ratios are equal. For example, the proportion
says that the ratios and are equal. In the proportion
a, b, c, and dare the termsof the proportion. The terms aand dare called the
extremes,and the terms band care called the means.We read the proportion
as “ais to bas cis to d.”Multiplying each side of this proportion by the common
denominator, bd, gives the following.
ab=
c
d1 where b, dZ 02 ,
a
b
=
c
d
15
203
43
4
=
15
20
A proportion is
a special type of
equation.Multiply each side by bd.Associative and commutative propertiesCommutative and identity propertiesWe can also find the products adand bcby multiplying diagonally.
ad bc
For this reason, adand bcare called cross products.
a
b
=
c
d
=
ad=bc
b
b
1 d#a 2 =
d
d
1 b#c 2
bd#
a
b
= bd#
c
d
Cross ProductsIf then the cross products adand bcare equal—that is, the product of the
extremes equals the product of the means.
Also, if ad= bc,then ba= dc 1 where b, dZ 02.
ab=
cd ,
NOW TRY
EXERCISE 2
A supermarket charges the
following prices for a certain
brand of liquid detergent.
Which size is the best buy?
What is the unit cost for
that size?
Size Price
150 oz $19.97
100 oz $13.97
75 oz $ 8.94NOW TRY ANSWER
2.75 oz; $0.119 per oz