Question

Can someone please help me with this math problem? ASAP. It’s a system of equations word problem. Can you please do the work where I can understand how to do it. Thank you.

Answer 1

Answer: A van can carry 18 students and a bus can carry 59 students.

Step-by-step explanation:

Let x represent the number of students that a van can carry.

Let y represent the number of students that a bus can carry.

The Senior class at high school A rented and filled one van and 6 buses with 372 students. This means that the number of students that entered the van is x × 1 = x.

Also, the number of students that entered the buses is y × 6 = 6y. Therefore,

x + 6y = 372 - - - - - - - - - - - - -1

The Senior class at high school B rented and filled 4 vans and 12 buses with 780 students. This means that the number of students that entered the vans is x × 4 = 4x.

Also, the number of students that entered the buses is y × 12 = 12y. Therefore,

4x + 12y = 780 - - - - - - - - - - - - -2

We would eliminate x by multiplying equation 1 by 4 and equation 2 by 1. It becomes

4x + 24y = 1488 - - - - - - - - - - - - -3

4x + 12y = 780 - - - - - - - - - - - - -4

Subtracting equation 4 from equation 3, it becomes

12y = 708

y = 708/12

y = 59

Substituting y = 59 into equation 1, it becomes

x + 6 × 59 = 372

x + 354 = 372

x = 372 - 354

x = 18