Question a-tota

1.3 Linear Equations in Two Variables - Writing equations from data/points
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A total of 2 squares each have side length r . A total of 6 equilateral triangles each have side length t . None of these squares and triangles shares a side. The sum of the perimeters of all these squares and triangles is 210 . Which equation represents this situation?

A.

6 r + 24 t = 210

B.

2 r + 6 t = 210

C.

8 r + 18 t = 210

D.

6 r + 2 t = 210

A total of 2 squares each have side length r . A total of 6 equilateral

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 a total of 2 squares each have side length r . Therefore, each of the squares has perimeter 4 r . Since there are a total of 2 squares, the sum of the perimeters of these squares is 4r+4r, which is equivalent to 24r, or 8 r . It’s also given that a total of 6 equilateral triangles each have side length t . Therefore, each of the equilateral triangles has perimeter 3 t . Since there are a total of 6 equilateral triangles, the sum of the perimeters of these triangles is 3t+3t+3t+3t+3t+3t, which is equivalent to 63t, or 18 t . Since the sum of the perimeters of the squares is 8 r and the sum of the perimeters of the triangles is 18 t , the sum of the perimeters of all these squares and triangles is 8r+18t. It’s given that the sum of the perimeters of all these squares and triangles is 210 . Therefore, the equation 8 r + 18 t = 210 represents this situation.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.