Question

Mrs. Adesso wants to take her class on a trip to either the science center or natural history museum. The science center charges $7 per student, plus $75 for a guided tour. The natural history museum charges $8 per student, plus $50 for a guided tour. For what number of students is the cost of the trip the same at each museum?

Answer 1

25

Explanation:

When we write expressions for the total cost of each field visit and set them equal, we find the solution to be the ratio of the difference in fixed cost to the difference in variable cost.

y = 75 +7x . . . . . cost for x students to visit the science center

y = 50 +8x . . . . cost for x students to visit the natural history museum

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Subtracting the first equation from the second, we get ...

0 = -25 +x

25 = x . . . . . add 25; the number of students such that costs are equal

The cost will be the same either place for 25 students.

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Additional comment

Here, the fixed cost difference is 75-50=25, and the variable cost difference is 8-7=1. The ratio of these costs is ...

$25/($1 /student) = 25 students.

This relationship only holds when the higher fixed cost is associated with the lower variable cost. Charges are such that one place caters to larger numbers of students (science center), and one prefers fewer students (natural history museum).