Question

The local amusement park is a popular fleld trip destination. This year the senior class at the High

School planned their senior class trip there. The school had to take 24 total vehides between vans
Vand buses. There are 752 total students in the senior class. Each van holds 8 students and each
bus can hold 43 students. How many vans and buses did they have to take?

Answer 1

• 8 vans
• 16 buses

Explanation:

The given relations can be written as two equations in two unknowns. These can be solved by any of the ususal methods.

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Setup

Let v and b represent the numbers of vans and buses used, respectively.

v + b = 24 . . . . . 24 vehicles were taken

8v +43b = 752 . . . . 752 students were transported

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Solution

Perhaps the easiest solution is that afforded by a graphing calculator. It shows the solution to be ...

v = 8 . . . . vans required

b = 16 . . . . buses required

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You can eliminate the v variable by subtracting 8 times the first equation from the second.

(8v +43b) -8(v +b) = (752) -8(24)

35b = 560 . . . . . simplify

b = 16 . . . . . . divide by 35

v = 24 -16 = 8 . . . . . find v from the first equation

They had to take 8 vans and 16 buses.