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. The equation $0 point 0 3 times, open parenthesis, 120 w, close parenthesis, plus, 0 point 1 8 times, open parenthesis, 180 z, close parenthesis, plus 3,385 point 8 0, equals 7,576 point 2 0.$ gives the total cost, in dollars, of the rocks used in the project in terms of the number of ft³of limestone, w, and the number of ft³ of basalt, z. All four rock types are used in the project. Which of the following is the best interpretation of 3,385.80 in this context?

A.

The cost of the sandstone needed for the project

B.

The cost of the basalt needed for the project

C.

The cost of the granite and sandstone needed for the project

D.

The cost of the basalt and limestone needed for the project

Accepted Answer

Choice A is correct. The table shows the cost of limestone is $0.03/lb, and the weight per volume for limestone is 120 lb/ft 3 . Therefore, the term represents the cost, in dollars, of w ft 3 of limestone. Similarly, the term represents the cost, in dollars, of z ft 3 of basalt. The given equation shows that the total cost of all the rocks used in the project is $7,576.20. Since it&rsquo;s given that all four rock types are used in the project, the remaining term, 3,385.80, represents the cost, in dollars, of the granite and sandstone needed for the project. Choice B is incorrect. The cost of basalt and limestone needed for the project can be represented by . Choice C is incorrect. The cost of the basalt needed for the project can be represented by the expression . Choice D is incorrect and may result from neglecting to include granite in the rock types used for the project.

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