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.
A circular wool quilt of 1.2 m diameter costs $200. What should the price of a 1.6-m-diameter quilt be if it is to have the same cost per unit area?
a. $110
b. $150
c. $270
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