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Hourly Wage

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RiyaR Rising GMAT Star Default Avatar
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Hourly Wage Post Wed Sep 24, 2014 7:52 am
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  • Lap #[LAPCOUNT] ([LAPTIME])
    . 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

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    Post Wed Sep 24, 2014 7:58 am
    Quote:
    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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    Thanked by: Harsh@rayal
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    Post Wed Sep 24, 2014 9:45 am
    Quote:
    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
    Another approach:

    Salary
    Mary's NET salary was x - y dollars (because Mary gave John y dollars)
    John's NET salary was x + y dollars

    Hours worked
    Mary worked 8 hours
    John worked 10 hours


    In the end, John and Mary received the SAME hourly wage.
    So, John's hourly wage = Mary's hourly wage
    Hourly wage = (total salary)/(hours worked)
    So, (x + y)/10 = (x - y)/8

    In terms of y, that John was paid in advance?
    In other words, what is the value of x (in terms of y)
    So, we'll solve our equation for x.

    Take (x + y)/10 = (x - y)/8 and cross multiply to get:
    10(x - y) = 8(x + y)
    Expand: 10x - 10y = 8x + 8y
    Rearrange: 2x = 18y
    Divide by 2: x = 9y
    So, John's advance payment = x = 9y = E

    Cheers,
    Brent

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