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1 June, 13:31

Select the correct answer. A dormitory manager buys 38 bed sheets and 61 towels for $791.50. The manager get another 54 bed sheets and 50 towels for $923 from the same store. What is the cost of one bed sheet and one towel? A. $15 and $10 B. $13.50 and $7.50 C. $12 and $5.50 D. $10.50 and $3

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  1. 1 June, 13:46
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    Okay, let's represent the price of a bed sheet with 'b' and a towel with 't':

    54b + 50t = 923

    38b + 61t = 791.50

    Now, if we subtract both sides by 54b (on the first equation), we get this:

    50t = 923 - 54b

    Divide both sides by 50:

    t = 18.46 - 1.08b

    Now that we know this, we can move on to the 2nd equation:

    38b + 61t = 791.50

    Input the variable 't':

    38b + 61 (18.46 - 1.08b) = 791.5

    38b + 1126.06 - 65.88b = 791.5

    38b - 65.88b = 791.5 - 1126.06

    Simplify:

    -27.88b = - 334.56

    Because both sides are negative, we can turn it into a positive:

    27.88b = 334.56

    b = 334.56/27.88

    b = 12

    Now that we know that b = 12, we can easily input it into any equation:

    648 + 50t = 923

    50t = 275

    t = 5.5

    One bed sheet costs $12 and one towel costs $5.50

    Option C is the answer.
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