Answer:
Explanation:
To determine when each service is a better deal without calculating the specific values for multiple values of n, you can use some general principles and a bit of algebra. Here's how you can approach it:
Set Up Inequalities: Compare the two services by setting up inequalities. Let's assume that "7 0.2n" represents the cost of Service A and "4 0.25n" represents the cost of Service B.
Identify the Variables: In this case, n is the variable that represents the quantity of the service you are purchasing.
Analyze the Inequalities:
For Service A (7 0.2n), you are paying $7 plus 20% of the quantity n.
For Service B (4 0.25n), you are paying $4 plus 25% of the quantity n.
Compare When Each Service is a Better Deal:
If you want to determine when Service A is a better deal, set up the inequality where the cost of A is less than the cost of B:
7 + 0.2n < 4 + 0.25n
Simplify the inequality:
0.2n - 0.25n < 4 - 7
-0.05n < -3
Divide by -0.05 (and reverse the inequality sign since you're dividing by a negative number):
n > 60
This means that for values of n greater than 60, Service A is a better deal.
If you want to determine when Service B is a better deal, set up the inequality where the cost of B is less than the cost of A:
4 + 0.25n < 7 + 0.2n
Simplify the inequality:
0.25n - 0.2n < 7 - 4
0.05n < 3
Divide by 0.05:
n < 60
This means that for values of n less than 60, Service B is a better deal.
So, you can determine when each service is a better deal without calculating specific values for n by setting up and analyzing these inequalities. For n values greater than 60, Service A is better, and for n values less than 60, Service B is better.