Answer:
The van can carry 8 students
The bus can carry 52 students
Explanation:
Assume that the number of students in each van is v and the number of students in each bus is b
∵ The senior class at Downingtown rented and filled 14 vans and
7 buses with 476 students
∵ The number of students in each van is v
∵ The number of students on each bus is b
∴ 14v + 7b = 476 ⇒ (1)
∵ West Chester HS rented and filled 7 vans and 11 buses with
628 students
∴ 7v + 11b = 628 ⇒ (2)
Let us solve this system of equations to find v and b
→ Multiply equation (2) by -2 to make the coefficients of v equal in
the values and different in the signs
∵ -2(7v) + -2(11b) = -2(628)
∴ -14v - 22b = -1256 ⇒ (3)
→ Now add equations (1) and (3) to eliminate v
∴ -15b = -780
→ Divide both sides by -15
∴ b = 52
→ Substitute the value of b in equation (1) to find v
∵ 14v + 52(7) = 476
∴ 14v + 364 = 476
→ Subtract 364 from both sides
∴ 14v = 112
→ Divide both sides by 14
∴ v = 8
The van can carry 8 students
The bus can carry 52 students