AAPL wrote:Official Guide
John and Mary were each paid \(x\) dollars in advance to do a certain job together. John worked on the job for 10 hours and mary worked for 2 hours less than John. If Mary gave John \(y\) dollars of her payment so that they would have received the same hourly wage, what was the dollar amount, in terms of \(y\), that John was paid in advance?
A. \(4y\)
B. \(5y\)
C. \(6y\)
D. \(8y\)
E. \(9y\)
Hourly wage = (total pay)/(total number of work-hours)
John worked on the job for 10 hours, and Mary worked for 2 hours less than John.
Thus, the total number of work-hours = 10+8 = 18.
John and Mary were each paid \(x\) dollars in advance.
Since the total pay should be divisible by the total number of work hours, let x = 18.
Since John and Mary are each paid $18 in advance, the total pay = 18+18 = 36.
Thus, the hourly wage = (total pay)/(total number of work-hours) = 36/18 = $2 per hour.
Since John works for 10 hours at a rate of $2 per hour, John's take-home pay = 10*2 = 20.
Since Mary works for 8 hours at a rate of $2 per hour, Mary's take-home pay = 8*2 = 16.
Mary gave John \(y\) dollars of her payment.
Since Mary is given $18 in advance but takes home $16, she gives John $2, implying that y=2.
What was the dollar amount, in terms of y, that John was paid in advance?
Since John was paid $18 in advance, the correct answer must yield 18 when y=2.
Only E works:
9y = 9*2 = 18
The correct answer is
E.
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