Question

All 231 students in the French class went on a field trip. Some students rode in vans which hold seven students each, and some students rode in buses which hold 25 students each. How many of each type of vehicle did they use if there were 15 vehicles total?

A) 11 vans and 4 buses
B) 10 vans and 5 buses
C) 9 vans and 6 buses
D) 8 vans and 7 buses

Answer 1

To solve this problem, we can use a system of equations. Let's assume that the number of vans used is 'v' and the number of buses used is 'b'. We can now solve this system of equations to find the values of v and b. So the answer is D) 8 vans and 7 buses were used.

Step-by-step explanation:

To solve this problem, we can use a system of equations. Let's assume that the number of vans used is 'v' and the number of buses used is 'b'.

We know that there were a total of 15 vehicles used, so we can write the equation: v + b = 15.

We also know that each van can hold 7 students and each bus can hold 25 students. So we can write another equation based on the total number of students:

7v + 25b = 231.

We can now solve this system of equations to find the values of v and b. Multiplying the first equation by 7, we have: 7v + 7b = 105. Subtracting this equation from the second equation, we get:

7v + 25b - (7v + 7b) = 231 - 105

18b = 126

Dividing both sides of the equation by 18, we find that b = 7. Substituting this value back into the first equation, we find that v = 8.

So the answer is D) 8 vans and 7 buses were used.