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 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
We can plug in a value for the hourly rate.
Let hourly rate = $1.
Since John works 10 hours, he earns 10*1 = $10.
Since Mary works 10-2=8 hours, she earns 8*1 = $8.
Thus, the total advance payment to John and Mary = 10+8 = $18.
Since each receives x dollars in advance, x = 18/2 = $9.
John is given x=9 in advance but must earn $10.
Mary is given x=9 in advance but must earn $8.
Thus, Mary gives John y=1.
The question asks for the amount that John is paid in advance: $9.
This is our target.
Now we plug y=1 into the answers to see which yields our target of 9.
Only answer choice E works:
9y = 9*1 = 9.
The correct answer is
E.
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