Final answer:
The number of hours, n, for which Ace's total charge is less than or the same as Acme's total charge is n ≤ 4.
Step-by-step explanation:
To find the number of hours, n, for which Ace's total charge is less than or the same as Acme's total charge, we need to compare the total charges from both companies.
Let's break down the charges for each company:
- Acme repair: Service call charge = $49, Charge per hour = $22.50
- Ace repair: Service call charge = $0, Charge per hour = $34.75
To find the total charge from each company, we can use the equation:
Total charge = Service call charge + (Charge per hour * Number of hours)
Let's represent the total charge from Acme as A and the total charge from Ace as B.
For Acme, the equation is:
A = 49 + (22.50 * n)
For Ace, the equation is:
B = 0 + (34.75 * n)
To find the number of hours, n, for which Ace's total charge is less than or the same as Acme's total charge, we can set up the inequality:
B ≤ A
Substituting the equations for A and B, we have:
34.75n ≤ 49 + 22.50n
Simplifying the inequality, we get:
12.25n ≤ 49
To solve for n, we divide both sides of the inequality by 12.25:
n ≤ 49/12.25
Calculating the value, we have:
n ≤ 4
Therefore, the number of hours, n, for which Ace's total charge is less than or the same as Acme's total charge is n ≤ 4.
Your question is incomplete, but most probably the full question was:
Billie needs to have her refrigerator repaired. She contacts two appliance companies and is given the rates shown in the table.
Acme repair- Service call charge: 49 Charge per hour: 22.50
Ace repair- Service call charge: 0 Charge per hour: 34.75
Q: Write an inequality that can be used to find the number of hours, n, for which Ace's total charge is less than or the same as Acme's total charge. Solve the inequality.