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14 October, 13:54

A business rents bicycles and in-line skates. Bicycle rentals cost $25 per day, and in-line skate rentals cost $20 per day. The business has 20 rentals today and makes $455. (Section 5.3) a. Write a system of linear equations that represents this situation. b. How many bicycle rentals and in-line skate rentals did the business have today

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  1. 14 October, 14:10
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    a.

    25 b+20 s=455 ... equation 1

    b+s=20 ... equation 2, where b and s are the number of bicycle and in-line skate rentals per day.

    b. The business had 11 bicycle rentals and 9 in-line skate rentals.

    Explanation:

    a.

    Step 1: Determine an equation for total revenue today

    Since the business rents bicycles and in-line skates, the total revenue will be as a result of amount received in revenue from renting the bicycles and in-line skates. This can be expressed as shown;

    T = (B*b) + (S*s)

    where;

    T=total revenue

    B=bicycle rental cost per day

    b=number of bicycles

    S=in-line skate rental cost per day

    s=number of in-line skates

    In our case;

    T=$455

    B=$25 per day

    b=unknown

    S=$20 per day

    s=unknown

    Replacing;

    (25*b) + (20*s) = 455

    25 b+20 s=455 ... equation 1

    Step 2: Determine an equation for total rentals today

    The equation for the total number of rentals is;

    R=b+s

    where;

    R=total number of rentals today

    b=number of bicycles

    s=number of in-line skates

    In our case;

    R=20

    b=unknown

    s=unknown

    Replacing;

    b+s=20 ... equation 2

    b.

    Step 3: Combine equation 1 and 2 ans solve simultaneously

    1 (25 b+20 s=455), multiplying equation 1 by 1=25 b+20 s=455

    20 (b+s=20), multiply equation 2 by 20=20 b+20 s=400

    25 b+20 s=455

    -

    20 b+20 s=400

    5 b+0 s=55

    (5 b) / 5=55/5=11

    b=11, replace the value for b in equation 2 and solve;

    (20*11) + 20 s=400

    220+20 s=400

    20 s=400-220=180

    20 s=180

    s = (180/20) = 9

    The business had 11 bicycle rentals and 9 in-line skate rentals.
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