Question

New York City is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 5 vans and 3 buses with 188 students. High School B rented and filled 10 vans and 5 buses with 340 students. Each van and each bus carried the same number of students. Find the number of students in each van and in each bus. A) Van: 6, Bus: 47 B) Van: 36, Bus: 16 C) Van: 16, Bus: 36 D) Van: 6, Bus: 50

Answer 1

Answer: There are 16 vans and 36 buses and Option 'c' is correct.

Step-by-step explanation:

Since we have given that

For high school A,

Number of vans = 5

Number of buses = 3

Number of students = 188

For high school B,

Number of vans = 10

Number of buses = 5

Number of students = 340

So, Let the number of students in van be 'x'

Let the number of students in bus be 'y'.

According to question, it becomes;

$5x+3y=188-----------------(1)\\\\10x+5y=340-------------------(2)$

So, first we do:

2(5x+3y=188)

10x+6y=376----------------(3)

So, from (2) and (3), we get that

$10x+6y=376\\\\10x+5y=340\\\\------------------------------\\\\y=36$

so, put the value of y = 36 in the eq(1), we get that

$5x+3\times 36=188\\\\5x+108=188\\\\5x=188-108\\\\5x=80\\\\x=16$

Hence, there are 16 vans and 36 buses and Option 'c' is correct.