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A plumber uses two different functions to model how much she charges for service calls.

For weekday service calls requiring [tex]$x$[/tex] hours of labor, the amount she charges, in dollars, is modeled by function [tex]$f$[/tex]: [tex]f(x) = 28x + 60[/tex]

For evening or weekend service calls requiring [tex]$x$[/tex] hours of labor, the amount she charges, in dollars, is modeled by function [tex]$g$[/tex]: [tex]g(x) = 50x + 75[/tex]

The function [tex]$\square$[/tex] represents the difference between the amount charged for a service call at 6 p.m. on a Saturday evening and a service call at 11 a.m. on a Tuesday morning.

For a service call lasting 3 hours, the difference in the amounts charged is [tex]$\$[/tex][tex]$ $[/tex]\square$



Answer :

GinnyAnswer
To solve this problem, let's follow these steps:

1. We have two functions to model the charges:
- For weekday service calls: [tex]\( f(x) = 28x + 60 \)[/tex]
- For evening or weekend service calls: [tex]\( g(x) = 50x + 75 \)[/tex]

2. We need to find out the charges for a service call lasting 3 hours. Let's substitute [tex]\( x = 3 \)[/tex] into each function.

3. Calculate the weekday charge using [tex]\( f(x) \)[/tex]:
[tex]\[ f(3) = 28 \times 3 + 60 = 84 + 60 = 144 \][/tex]

4. Calculate the evening/weekend charge using [tex]\( g(x) \)[/tex]:
[tex]\[ g(3) = 50 \times 3 + 75 = 150 + 75 = 225 \][/tex]

5. To find the difference between the charges, subtract the weekday charge from the evening/weekend charge:
[tex]\[ g(3) - f(3) = 225 - 144 = 81 \][/tex]

So, the function [tex]\( g(x) - f(x) \)[/tex] represents the difference in charges, and for a service call lasting 3 hours, the difference in the amounts charged is [tex]$\$[/tex]81[tex]$. Thus, the correct answers are: - The function \( g(x) - f(x) \) represents the difference between the amount charged for a service call at 6 p.m. on a Saturday evening and a service call at 11 a.m. on a Tuesday morning. - For a service call lasting 3 hours, the difference in the amounts charged is \$[/tex]81.

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