For what value of a do the two expressions give the same amount of water for every value of w?

Question

In a rooftop greenhouse, the water used by the north bed during a growing period of w weeks is given by 2(6w - 9) + a liters, and the water used by the south bed during the same period is given by 3(4w + 5) - 11 liters, where a is a constant.

Accepted Answer

C. 22. Distributing gives 12w - 18 + a on the left and 12w + 15 - 11 = 12w + 4 on the right. The w-terms already match, so the equation 12w - 18 + a = 12w + 4 holds for every w exactly when the constants match: -18 + a = 4, so a = 22. Choice B encodes matching a to the right-side constant while forgetting the -18 from distributing 2(6w - 9). Choice A encodes the sign error a = 4 - 18 instead of a = 4 + 18. Choice D encodes forgetting the -11 on the right side, giving a = 15 + 18 = 33.

Answer

A. -14 — You computed 4 - 18 instead of 4 + 18; moving the -18 to the other side of -18 + a = 4 means adding 18, so a = 22.

Answer

B. 4 — You matched a to the right side's constant of 4, but distributing 2(6w - 9) leaves a -18 on the left, so the left constant is a - 18, not a.

Answer

D. 33 — You used 15 as the right-side constant and forgot to subtract the 11, so 3(4w + 5) - 11 gives a constant of 4, not 15.

Algebra practice question

Answer: C. 22

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