Question

The water park charges a $45 fee plus $5 per student for a field trip. The bowling alley charges a $35 fee plus $7 per student. The lines in the graph represent the cost of each field trip.

For what number of students will the total cost of each field trip be the same, and what will that cost be?

A graph of the first quadrant consisting of one red line and one blue line intersecting each other at a point at which the x intercept is 5 units and the y intercept is 70 units. Title. Text that reads: Field Trip Costs. Red line. Text that reads: y = 35 + 7x. Blue line. Text that reads: y = 45 + 5x. X axis. Text that reads: Number of students. Y axis. Text that reads: Cost ($).
A.
For 10 students, the cost will be the same, and the cost will be $105.
B.
For 70 students, the cost will be the same, and the cost will be $5.
C.
For 5 students, the cost will be the same, and the cost will be $70.
D.
For 105 students, the cost will be the same, and the cost will be $10.

Answer 1

For 5 students, both the water park and bowling alley field trips have the same cost of $70, as represented by the point of intersection (5, 70) on the graph. So the correct option is C.

The point of intersection on the graph represents the number of students at which the total cost for both field trips is the same. Setting the cost equations equal to each other,
`\(45 + 5x = 35 + 7x\)`, allows us to find this point. Simplifying,
`\(2x = 10\)`, we get
`\(x = 5\).` Therefore, for 5 students, the total cost is equal for both the water park and the bowling alley. Substituting this value back into either cost equation gives us the common cost. Using the water park equation
`\(C_1 = 45 + 5x\),` the cost is
`\(C_1 = 45 + 5(5) = 70\).` Hence, for 5 students, the total cost for both field trips is $70.

The answer is option C: For 5 students, the cost will be the same, and the cost will be $70. This interpretation is crucial in understanding the point of intersection on the graph and providing a meaningful solution to the problem, as it aligns with the coordinates (5, 70) on the graph.