Question

The local amusement park is a popular field trip destinations. This year the senior class at high school a and the senior class in high school b both planned trips there. The senior class at high school a rented And filled 16 vans and 8 buses with 752 students. High school b rented and filled 5 vans and 5 buses with 380 students. each van and each bus carried the same number of students. How many students Can a van Carry? How many students can a bus carry?

Answer 1

Van = 18

Bus = 58

Explanation:

Let v be the number of students carried by each van.

Let b be the number of students carried by each bus.

We know the following:

`$\left\{{{16v+8b=752}\atop{5v+5b=380}}$`

Solve the second equation for b:

`$5v+5b=380$`

`$5b=380-5v$`

`$b=76-v$`

Replace b with (76 – v) in the first equation:

`$16v+8b=752$`

`16v+8(76-v)=752`

`16v+608-8v=752`

`8v+608=752`

`8v=144`

`v=18`

Therefore, each van can carry 18 students. Each bus, then, can carry 76 – v = 76 – 18 = 58.

To verify:

High School A had 16 vans and 8 buses equaling (16 × 18) + (8 × 58) = 288 + 464 = 752. That is correct.

High School B had 5 vans and 5 buses equaling (5 × 18) + (5 × 58) = 90 + 290 = 380. That is correct.