Katy wants to enroll in art school. School A charges a monthly charge of $17.50 and a one-time enrollment fee of $55. School B charges a monthly charge of $12.50 and a one-time enrollment fee of $95. Which inequality can be used to find x, the maximum number of months Katy is enrolled so that the total charge of School A is less than the total charge of School B?
a 17.5x + 55 > 12.5x + 95
b 17.5x + 95 < 12.5 + 55
c 17.5 - 55 < 12.5 - 95
d 17.5x + 55 < 12.5x + 95
The correct inequality to find x, the maximum number of months Katy is enrolled so that the total charge of School A is less than the total charge of School B is:
a 17.5x + 55 > 12.5x + 95
To determine the inequality, we need to compare the total charges of School A and School B.
For School A, the total charge is the sum of the monthly charge and the one-time enrollment fee: 17.5x + 55.
For School B, the total charge is the sum of the monthly charge and the one-time enrollment fee: 12.5x + 95.
Since we want the total charge of School A to be less than the total charge of School B, the correct inequality is:
17.5x + 55 < 12.5x + 95
Therefore, option d: 17.5x + 55 < 12.5x + 95 is the correct inequality to find the maximum number of months Katy can be enrolled so that School A's total charge is less than School B's total charge.
To find the inequality that can be used to find the maximum number of months Katy can be enrolled so that the total charge of School A is less than the total charge of School B, we need to compare the total charges of both schools.
Let's break down the charges for each school first:
School A:
- Monthly charge: $17.50
- One-time enrollment fee: $55
School B:
- Monthly charge: $12.50
- One-time enrollment fee: $95
Now, let's calculate the total charges for each school based on the given information:
Total charge for School A = (Monthly charge * Number of Months) + One-time enrollment fee
Total charge for School B = (Monthly charge * Number of Months) + One-time enrollment fee
To find the inequality, we need to compare these two total charges:
Total charge for School A < Total charge for School B
Now, let's substitute the values and simplify the inequality:
(17.5x + 55) < (12.5x + 95)
Therefore, the correct inequality that can be used to find the maximum number of months Katy is enrolled so that the total charge of School A is less than the total charge of School B is:
a) 17.5x + 55 > 12.5x + 95