A school is preparing a trip for 400 students. The company who is providing the transportation has 10 buses of 50 seats each and 8 buses of

Question

A school is preparing a trip for 400 students. The company who is providing the transportation has 10 buses of 50 seats each and 8 buses of 40 seats, but only has 9 drivers available. The rental cost for a large bus is $800 and $600 for the small bus. Calculate how many buses of each type should be used for the trip for the least possible cost. Let x = the small buses and y= the big buses.

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Ayla 1 week 2021-09-09T05:44:33+00:00 1 Answer 0

Answers ( )

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    2021-09-09T05:46:03+00:00

    The number of small buses used = 5

    The number of big buses used  = 4

    Step-by-step explanation:

    Let us assume the total number of small buses needed = x

    The capacity of 1 small bus  = 40

    So, the capacity of x buses  = 40(x)  = 40 x

    Let us assume the total number of big buses needed = y

    The capacity of 1 big bus  = 50

    So, the capacity of y buses  = 50(y)  = 50 y

    Also, the total students travelling = 400

    So, the number of students traveling by (Small bus + Big bus)  = 400

    40 x + 50 y = 400 ….. (1)

    Also, the total number of drivers available  = 9

    x +  y = 9  ….. (2)

    Also, x  ≤ 8,   y ≤ 10

    Now, solving both equations, we get:

    40 x + 50 y = 400 ….. (1)

    x +  y = 9  ⇒ y = (9-x) put in (1)

    40 x + 50 y = 400  ⇒  40 x  + 50 (9-x)  = 400

    or, 40 x  + 450 – 50 x  = 400

    or, – 10 x  =- 50

    or, x  = 5 y = (9-x)  = 9- 5 = 4

    Hence the number of small buses used = 5

    The number of big buses used  = 4

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