For what value of k is there no value of s for which the two expressions are equal?

Question

At the Marlin Swim Club, the total seasonal cost, in dollars, of Plan A for s swim sessions is given by the expression 5(s + 9), and the total seasonal cost of Plan B is given by the expression ks + 3(s + 10), where k is a constant.

Accepted Answer

B. 2. Setting the expressions equal gives 5s + 45 = ks + 3s + 30, or 5s + 45 = (k + 3)s + 30. The equation has no solution exactly when the s-coefficients are equal but the constants are not: k + 3 = 5 gives k = 2, and then 45 = 30 is false, so no value of s works. (For any other k, s = 15/(k - 2) is a solution.) Choice C encodes ignoring the 3s produced by distributing 3(s + 10) and simply setting k = 5. Choice D encodes solving k + 3 = 5 by adding 3 instead of subtracting. Choice A encodes the sign error k = 3 - 5.

Answer

A. -2 — You got k = 3 - 5 instead of k = 5 - 3; from k + 3 = 5 you subtract 3 from 5, giving k = 2.

Answer

C. 5 — You set k = 5 by matching k directly to the 5 on the left, but distributing 3(s + 10) gives an extra 3s, so the s-coefficient on the right is k + 3, not k.

Answer

D. 8 — You solved k + 3 = 5 by adding 3 to 5 instead of subtracting 3 from it; the correct value is k = 2.

Algebra practice question

Answer: B. 2

Why the other answers are wrong

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