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Difficulty: Medium
Characteristics for Rock Types
Rock typeWeight per volume (lb/ft3)Cost per pound
Basalt180$0.18
Granite165$0.09
Limestone120$0.03
Sandstone135$0.22
 

A city is planning to build a rock retaining wall, a monument, and a garden in a park. The table above shows four rock types that will be considered for use in the project. Also shown for each rock type is its weight per volume, in pounds per cubic foot (lb/ft3), and the cost per pound, in dollars. Only basalt, granite, and limestone will be used in the garden. The rocks in the garden will have a total weight of 1,000 pounds. If 330 pounds of granite is used, which of the following equations could show the relationship between the amounts, x and y, in ft3, for each of the other rock types used?

 

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Explanation

Choice C is correct. It’s given that the weight of the granite used in the garden is 330 pounds. The weight of the limestone used in the garden is a product of its weight per volume, in lb/ft3, and its volume, in ft3. Therefore, the weight of the limestone used in the garden can be represented by 120 x, where x is the volume, in ft3, of the limestone used. Similarly, the weight of the basalt used in the garden can be represented by 180 y, where y is the volume, in ft3, of the basalt used. It’s given that the total weight of the rocks used in the garden will be 1,000 pounds. Thus, the sum of the weights of the three rock types used is 1,000 pounds, which can be represented by the equation 120 x, plus 180 y, plus 330, equals 1,000. Subtracting 330 from both sides of this equation yields 120 x, plus 180 y, equals 670.

Choice A is incorrect. This equation uses the weight per volume of granite instead of limestone. Choice B is incorrect. This equation uses the weight per volume of granite instead of basalt, and doesn’t take into account the 330 pounds of granite that will be used in the garden. Choice D is incorrect. This equation doesn’t take into account the 330 pounds of granite that will be used in the garden.