Smoky Hill DECA and Grandview DECA are both heading down to the state finals in Colorado Springs. Smoky Hill took 8 vans and 8 mini-busses with 240 students while Grandview took 4 vans and 1 mini-bus for a total of 54 students. How many students does a van Hold? How many students does a mini-bus hold?

number of students in a van = 8

number of students in a minibus = 22

Step-by-step explanation:

Let

x = number of students in a van

y = number of students in a minibus

8x + 8y = 240 (1)

4x + y = 54 (2)

Multiply (2) by 8 to eliminate y

4x + y = 54 ×8

32x + 8y = 432 (3)

8x + 8y = 240 (1)

32x + 8y = 432 (3)

Subtract (1) from (3)

32x - 8x = 432 - 240

24x = 192

Divide both sides by 24

x = 192 / 24

= 8

x = 8 students

Substitute x = 8 into (2)

4x + y = 54

4(8) + y = 54

32 + y = 54

y = 54 - 32

= 22

y = 22 students

number of students in a van = 8

number of students in a minibus = 22

∠cbe and ∠deb are same-side interior angles.

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