Which ordered pair (x, y) satisfies both conditions?

Question

A school robotics club is buying parts for a competition. Sensors cost $12 each and motors cost $20 each. The club can spend no more than $200 in total, and it must buy at least 8 parts altogether. If x is the number of sensors and y is the number of motors purchased, then 12x + 20y ≤ 200 and x + y ≥ 8.

Accepted Answer

B. (5, 5). For (5, 5): 12(5) + 20(5) = 60 + 100 = 160 ≤ 200, and 5 + 5 = 10 ≥ 8, so both conditions hold. Choice A satisfies the cost condition (36 + 80 = 116) but has only 3 + 4 = 7 parts, so it fails the 'at least 8 parts' condition — the error of checking the budget only. Choice C has 13 parts but costs 72 + 140 = 212 > 200, the error of checking the part count only. Choice D costs 24 + 180 = 204 > 200; it appears to work only if the prices are swapped (12·9 + 20·2 = 148), the error of attaching each price to the wrong variable.

Answer

A. (3, 4) — The cost works (36 + 80 = 116 ≤ 200), but you didn't check the second condition: 3 + 4 = 7 parts, which is fewer than the required 8.

Answer

C. (6, 7) — You checked the part count (6 + 7 = 13 ≥ 8) but not the cost: 12(6) + 20(7) = 212, which is over the $200 limit.

Answer

D. (2, 9) — This only works if you attach the prices to the wrong variables. With sensors at $12 and motors at $20, the cost is 12(2) + 20(9) = 204, which exceeds $200.

Algebra practice question

Answer: B. (5, 5)

Why the other answers are wrong

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