Concept explainers
Using proportions A proportion is defined as an equality between two ratios; for instance, a/b = c/d. Proportions can be used to determine the expected change in one quantity when another quantity changes Suppose, for example, that the speed of a car doubles By what factor does the stopping distance of the car change? Proportions can also be used to answer everyday questions, such as whether a large container or a small container of a product is a better buy on a cost-per-unit-mass basis.
Suppose that a small pizza costs a certain amount. How much should a larger pizza of the same thickness cost? If the cost depends on the amount of ingredients used, then the cost should increase in proportion to the pizza s area and not in proportion to its diameter:
Let us rearrange Eq. (3.10) so the two variable quantities (cost and radius) are on the right side of the equation and the constants are on the left:
This equation should apply to any size pizza. If r increases, the cost should increase so that the ratio Cost/r2 remains constant. Thus, we can write a proportion for pizzas of different sizes:
For example, if a 3.5-in. -radius pizza costs $4.00, then a 5.0-in. radius pizza should cost.
This process can be used for most equations relating two quantities that change while all other quantities remain constant.
You decide to open a pizza parlor The ingredients require that you charge $4.50 for a 7.0-in -diameter pizza How large should you make a pizza whose price is $10.00, assuming the cost is based entirely on the cost of ingredients?
a. 1.4 in.
b. 3.1 in.
c. 7.0 in.
d. 10 in.
e. 16 in.
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