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The agriculture classes from Sheridan and Heights took a field trip to the state fair.
Heights filled 8 vans and 8 buses with 240 students. Sheridan filled 4 vans and 1 bus
with 54 students. Every van had the same number of students in it as did the buses.
Find the number of students in each van and in each bus.

Question

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Respuesta :

absor201 absor201 · Answer 1 · 2020-01-19T10:23:14+01:00

There are 8 students in each van and 22 students in each bus.

Step-by-step explanation:

Let,

x be the number of students in each van

y be the number of students in each bus

According to given statement;

8x+8y=240 Eqn 1

4x+y=54 Eqn 2

Multiplying Eqn 2 by 2

[tex]2(4x+y=54)\\8x+2y=108\ \ \ Eqn\ 3\\[/tex]

Subtracting Eqn 3 from Eqn 1

[tex](8x+8y)-(8x+2y)=240-108\\8x+8y-8x-2y=132\\6y=132[/tex]

Dividing both sides by 6

[tex]\frac{6y}{6}=\frac{132}{6}\\y=22[/tex]

Putting y=22 in Eqn 2

[tex]4x+22=54\\4x=54-22\\4x=32\\[/tex]

Dividing both sides by 4

[tex]\frac{4x}{4}=\frac{32}{4}\\x=8[/tex]

There are 8 students in each van and 22 students in each bus.

Keywords: linear equation, elimination method

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