Question charac
| 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?
Characteristics for Rock Types Rock type Weight per volume (lb/ft 3 ) Cost per pound Basalt
Hard-difficulty · SAT Math · Linear Equations in Two Variables — Writing equations from data/points. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.
Answer explanation
Choice C is correct. It’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/ft3, and its volume, in ft3. Therefore, the weight of the limestone used in the can be represented by 
, where x is the volume, in ft3, of the limestone used. Similarly, the weight of the basalt used in the can be represented by 
, where y is the volume, in ft3, of the basalt used. It’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’t take into account the 330 pounds of granite that will be used in the . Choice D is incorrect. This equation doesn’t take into account the 330 pounds of granite that will be used in the .
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