How many students can fit into one bus and one van

Question

-The senior classes at West High School and North High School planned separate trips to the state fair. The senior class at West High School rented and filled 10 vans and 6 buses with 276 students. North High School rented and filled 5 vans and 2 buses with 117 students. Each van had the same number of students and each van had the same number of students.

A. How many students were in a single van?

B. How many students were in a single bus?

Answer 1

We translate what we know from English to algebra.

10 times the number of vans plus 6 times the number of buses equals 276.

10v + 6b = 276

5 times the number of vans plus 2 times the number of buses equals 117.

5v + 2b = 117

We then solve one equation for a variable.

v = 27.6 - 0.6b

And substitute this into the other equation

5 ( 27.6 - 0.6b ) + 2b = 117

And solve for b

138 - 3b + 2b = 117

138 - b = 117

-b = -21

b = 21

We put this back into our equation:

v = 27.6 - 0.6b

v = 27.6 - 0.6 ( 21 )

v = 27.6 - 12.6

v = 15

Our answer is

A. 15 students in each van

B. 21 students in each bus

We can check our answer by putting these values into the original equations and checking if they are true.

10v + 6b = 276

10 ( 15 ) + 6 ( 21 ) = 276

150 + 126 = 276

276 = 276 TRUE!

5 ( 15 ) + 2 ( 21 ) = 117

75 + 42 = 117

117 = 117 TRUE!