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Lionel uses two functions to model the costs of having a problem diagnosed and repaired by two appliance repair companies.

He models the cost, in dollars, of having Phil's Appliances handle the repair job, requiring [tex]$x$[/tex] hours of labor, with function [tex]$p$[/tex]: [tex]$p(x)=68x+81$[/tex].

He models the cost of having Quality Electric handle the same repair with function [tex][tex]$q$[/tex][/tex]: [tex]$q(x)=51x+90$[/tex].

The function [tex]\square[/tex] represents the amount, in dollars, Lionel will save by having Quality Electric handle an [tex]$x$[/tex]-hour repair instead of Phil's Appliances.

Lionel will save [tex][tex]$\$[/tex]$ \square[/tex] if he uses Quality Electric for a repair needing 2 hours of labor.



Answer :

GinnyAnswer
Sure, let's solve this step-by-step.

1. Identify the cost functions:
- The cost for Phil's Appliances is modeled by the function [tex]\( p(x) = 68x + 81 \)[/tex].
- The cost for Quality Electric is modeled by the function [tex]\( q(x) = 51x + 90 \)[/tex].

2. Determine the function that represents the savings:
- The savings Lionel will have by using Quality Electric instead of Phil's Appliances is the difference between the costs of Phil's Appliances and Quality Electric. This can be represented by the function:
[tex]\( s(x) = p(x) - q(x) \)[/tex].

3. Calculate the savings function explicitly:
- Substituting the given functions into the savings function:
[tex]\[ s(x) = (68x + 81) - (51x + 90) = 68x + 81 - 51x - 90 \][/tex]
- Combining like terms:
[tex]\[ s(x) = 68x - 51x + 81 - 90 = 17x - 9 \][/tex]

4. Calculate the savings for 2 hours of labor:
- Substitute [tex]\( x = 2 \)[/tex] into the savings function:
[tex]\[ s(2) = 17(2) - 9 = 34 - 9 = 25 \][/tex]

5. Fill in the blanks:
- The function [tex]\( s(x) = 17x - 9 \)[/tex] represents the amount, in dollars, Lionel will save by having Quality Electric handle an [tex]\( x \)[/tex]-hour repair instead of Phil's Appliances.
- Lionel will save \[tex]$25 if he uses Quality Electric for a repair needing 2 hours of labor. Thus, the selected answers should be: - The function \(\boxed{s(x) = 17x - 9}\) represents the amount, in dollars, Lionel will save by having Quality Electric handle an \( x \)-hour repair instead of Phil's Appliances. - Lionel will save \$[/tex][tex]\(\boxed{25}\)[/tex] if he uses Quality Electric for a repair needing 2 hours of labor.

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