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Linear equations in two variables SAT question

Math · Algebra · Easy · Answer it here, explanation included.

 
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. 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 ft3 of 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?

ExplanationShow

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/ft3. Therefore, the term 0 point 0 3 times 120 w represents the cost, in dollars, of w ft3 of limestone. Similarly, the term 0 point 1 8 times 180 z represents the cost, in dollars, of z ft3 of basalt. The given equation shows that the total cost of all the rocks used in the project is $7,576.20. Since it’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 0 point 1 8 times 180 z, plus, 0 point 0 3 times 120 w. Choice C is incorrect. The cost of the basalt needed for the project can be represented by the expression 0 point 1 8 times 180 z. Choice D is incorrect and may result from neglecting to include granite in the rock types used for the project.

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