Question

A museum charges a yearly membership fee plus an additional price per visit. Brian visited the museum eight times and paid a total of $175. Samantha visited the museum 13 times and paid a total of $235. What is the annual membership fee and the price per visit? Be sure to define your variables and solve algebraically.

Answer 1

Answer:

x = annual membership fee = $79

y = price per visit = $12

Step-by-step explanation:

Let

x = annual membership fee

y = price per visit

Brian:

x + 8y = 175

Samantha:

x + 13y = 235

x + 8y = 175 (1)

x + 13y = 235 (2)

Subtract (1) from (2) to eliminate x

13y - 8y = 235 - 175

5y = 60

y = 60/5

y = 12

Substitute y = 12 into (1)

x + 8y = 175 (1)

x + 8(12) = 175

x + 96 = 175

x = 175 - 96

x = 79

x = annual membership fee = $79

y = price per visit = $12