Characteristics for Rock Types Rock type Weight per volume (lb/ft 3 ) Cost per pound Basalt 180 $0.18 Granite 165

Question

Characteristics for Rock Types
Rock type	Weight per volume (lb/ft³)	Cost per pound
Basalt	180	$0.18
Granite	165	$0.09
Limestone	120	$0.03
Sandstone	135	$0.22

A city is planning to build a rock retaining wall, a monument, and a 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 . The rocks in the 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?

Accepted Answer

Choice C is correct. It&rsquo;s given that the weight of the granite used in the is 330 pounds. The weight of the limestone used in the is a product of its weight per volume, in lb/ft 3 , and its volume, in ft 3 . Therefore, the weight of the limestone used in the can be represented by , where x is the volume, in ft 3 , of the limestone used. Similarly, the weight of the basalt used in the can be represented by , where y is the volume, in ft 3 , of the basalt used. It&rsquo;s given that the total weight of the rocks used in the 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 . Subtracting 330 from both sides of this equation yields . 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&rsquo;t take into account the 330 pounds of granite that will be used in the . Choice D is incorrect. This equation doesn&rsquo;t take into account the 330 pounds of granite that will be used in the .

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