Foundations of Math II: 6.3 - Problem 12

[mukesh.mulchandani]

Salesperson A’s compensation for any week is $360 plus 6% of the portion of A’s total sales above $1,000 for that week. Salesperson B’s compensation for any week is 8 percent of B’s total sales for that week. For what amount of total weekly sales would both salespeople earn the same compensation?

And below is answer explanation as given by MGMAT. I believe the equations are constructed incorrectly. See highlighted text above. Am I missing something? I do not have OG 12 to compare the answer.

Variables:

a = salesperson A’s total compensation
b = salesperson B’s total compensation
s = total sales for that week

Note that you only need one variable for total sales -- because you are looking for A and B to sell the SAME amount & earn the same commission.

Equations:

a = 360 + 0.06(s - 1,000)
b = 0.08(s)

Combine and solve:

360 + 0.06(s - 1,000) = 0.08s
360 + 0.06s - 60 = 0.08s
300 = 0.02s

s = 300/0.02 = 30,000/2 = 15,000

This problem is #114 from the Official Guide to GMAT Review, Quantitative Supplement, published by the Graduate Management Admission Council.

[tim]

looks fine to me. can you be more specific about what you think the problem is?

[mukesh.mulchandani]

Based on highlighted wording in the problem I expect equations to be

a = 360 + 0.06(sa - 1,000)
b = 0.08(sb)

where
sa = A's total sales for that week
sb = B's total sales for that week

[tim]

sure, but they want to know what single amount for both A and B will make the compensation equal, which is why we use the same variable..

[mukesh.mulchandani]

Aah, I get it now. Thanks.

[tim]

cool :)