Question

The water park is a popular field trip destination. This year the senior class at high school a and high school b both planned trips there. The senior class at high school a rented filled 4 vans and 14 buses with 742 students. High school b rented and filled 4 vans and 6 buses with 350 students. Each van and each bus carried the same number of students. Find the number of students in each van and in each bus.

Answer 1

so let’s start of by setting variables for buses and vans
x = buses
y = vans

our equations will look something like this :

4x + 14y = 742 &’
4x + 6y = 350

let’s solve for y first . we need to cancel out our x’s so we turn on of them into a negative and since both of them have the same common factor we don’t need to find it . let’s multiply the bottom equation by ( -1 )

here’s what our new equations look like :
4x + 14y = 742
-4x - 6y = -350

now that our x’s are cancelled out we add our y’s and our totals :

14y + ( -6y ) = 8y
742 + ( -350 ) = 392

we want y alone so we divide :

392/8 = 49

y = 49

now we can substitute 49 for y :

4x + 14 ( 49 ) = 742
4x + 6 ( 49 ) = 350

we can multiply those numbers together :

4x + 686 = 742
4x + 294 = 350

now we add downward :

8x + 980 = 1,092

we need x alone so we subtract 980 from both sides :

8x = 112

divide by 8 :

x = 14

now , we can substitute 14 for x and 49 for y to check our work :

4 ( 14 ) + 14 ( 49 ) = 742

742 = 742 ✅

4 ( 14 ) + 6 ( 49 ) = 350

350 = 350 ✅