All 231 students in the math club went on a field trip in 15 vehicles. Some students rode in vans which holds 7 students each and some students ride in buses which holds 25 students each. How many vans and buses were used?

All 231 students in the math club went on a field trip in 15 vehicles
Some students rode in vans which holds 7 students each and some students ride in buses which holds 25 students each

We need to find how many vans and buses were used

Assume that the number of vans is x and the number of buses is y

∵ There were x vans in the trip

∵ There were y buses in the trip

∵ They went in 15 vehicles

- Add x and y and equate the sum by 15

∴ x + y = 15 ⇒ (1)

∵ Each van holds 7 students

∵ Each bus holds 25 students

∵ 231 students went to the trip

- Multiply x by 7 and y by 25, then add the products and equate

the sum by 231

∴ 7x + 25y = 231 ⇒ (2)

Now we have a system of equation to solve it

Multiply equation (1) by -7 to eliminate x

∵ -7x - 7y = -105 ⇒ (3)

- Add equations (2) and (3)

∴ 18y = 126

- Divide both sides by 18

∴ y = 7

- Substitute the value of y in equation (1) to find x

∵ x + 7 = 15

- Subtract 7 from both sides

∴ x = 8

They used 8 vans and 7 buses

Learn more:

You can learn more about the system of equations in brainly.com/question/6075514

#LearnwithBrainly