Question

A school transports its 105 students on field trips by a combination of cars and vans. On a field trip to an art museum, the students filled 14 cars and 5 vans. On a field trip to a nature preserve, the students filled 7 cars and 10 vans. Choose the equations that can be used to find the number of students that can fit in a car, x, and the number of students that can fit in a van, y.

Option 1:
A. 7x + 5y = 105
14x - 5y = 105

Option 2:
B. 14x + 7x = 105
5y + 10 = 105

Option 3:
C. 14x + 5y = 105
7x + 10y = 105

Option 4:
D. 19x + 17y = 105
9x - 5y = 105

Correct Option:
Option 1: A. 7x + 5y = 105
14x - 5y = 105

Answer 1

The correct equations in this context, to find the number students per car, x, and per van, y, when a total of 105 students are transported, is represented by 14x + 5y = 105 and 7x + 10y = 105, found in Option 3: C.

Step-by-step explanation:

The correct equations to find the number of students that can fit in a car, x, and the number of students that can fit in a van, y, given the information that a school transports its 105 students on field trips by a combination of cars and vans, are found in Option 3: C. On one trip there were 14 cars and 5 vans, and on another trip, there were 7 cars and 10 vans, which can be represented as the system of equations:

• For the art museum trip with 14 cars and 5 vans: 14x + 5y = 105
• For the nature preserve trip with 7 cars and 10 vans: 7x + 10y = 105

These equations can be used to solve for x and y simultaneously.