Question

A camp program charges a registration fee and a daily amount. The total bill for one camper was $338 for 12 days and the total bill for another camper was $506 for 19 days. Find the equation that gives the cost of the camp, y, in terms of the number of days at camp, x.

A. y = 20x + 98
B. y = 22x + 74
C. y = 28x + 32
D. y = 25x + 25

Answer 1

After setting up a system of equations based on the given information ($338 for 12 days and $506 for 19 days) and solving for the daily rate and registration fee, the correct equation representing the total cost of the camp should be y = 24x + 50, which is not among the provided options.

Step-by-step explanation:

The goal is to find the equation that represents the total cost of the camp, y, in terms of the number of days at the camp, x. Given two sets of values, ($338 for 12 days and $506 for 19 days), we can set up a system of equations to determine the registration fee and the daily amount.

To solve this, let's set up the two equations based on the given information:

1. y = ax + b (a = daily rate, b = registration fee)
2. 338 = 12a + b
3. 506 = 19a + b

Subtracting the second equation from the third gives us a system that we can solve:

1. 506 - 338 = 19a - 12a
2. 168 = 7a
3. a = 24

Using the value of a in either the second or third equation to find b gives us:

1. 338 = 12(24) + b
2. 338 = 288 + b
3. b = 50

Therefore, the equation representing the total cost of the camp in terms of the number of days at camp is y = 24x + 50, which is not included in the multiple choice options provided by the student. The options given are incorrect based on our calculations.