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Cynthia was offered two different jobs for the summer.

Working as a camp counselor, she will earn [tex]$\$[/tex]10[tex]$ per hour plus an additional $[/tex]\[tex]$50$[/tex] bonus. Her earnings after [tex]$x$[/tex] hours can be represented by the function [tex]$F(x)=10x+50$[/tex].

Working as a lifeguard, Cynthia will earn [tex]$\$[/tex]15[tex]$ per hour and an additional $[/tex]\[tex]$25$[/tex] bonus. Her earnings after [tex]$x$[/tex] hours can be represented by the function [tex]$g(x)=15x+25$[/tex].

The arithmetic operation [tex]$(f-g)(x)$[/tex] can be used to determine the difference in the salary Cynthia will earn working as a camp counselor instead of a lifeguard after [tex]$x$[/tex] hours.

What is the function [tex]$(f-g)(x)$[/tex]?

A. [tex]$(f-g)(x) = -5x + 25$[/tex]
B. [tex]$(f-g)(x) = -5x + 75$[/tex]
C. [tex]$(f-g)(x) = 25x + 25$[/tex]
D. [tex]$(f-g)(x) = 25x + 75$[/tex]



Answer :

GinnyAnswer
To determine the difference in Cynthia's earnings between working as a camp counselor and as a lifeguard, we need to subtract the lifeguard earnings function from the camp counselor earnings function.

Here's the step-by-step process:

1. Define the earnings functions:
- As a camp counselor: \( f(x) = 10x + 50 \)
- As a lifeguard: \( g(x) = 15x + 25 \)

2. Determine the difference in earnings functions:
- We want to find \( (f - g)(x) \), which means we need to subtract \( g(x) \) from \( f(x) \).

3. Perform the subtraction:
- \( (f - g)(x) = f(x) - g(x) \)
- Substitute the given functions into the expression: \( f(x) - g(x) = (10x + 50) - (15x + 25) \)

4. Simplify the expression:
- Distribute the subtraction: \( (10x + 50) - (15x + 25) \)
- Combine like terms: \( 10x - 15x + 50 - 25 \)
- Simplify further: \( -5x + 25 \)

Therefore, the function representing the difference in Cynthia's earnings when working as a camp counselor instead of a lifeguard after \( x \) hours is:

[tex]\[ (f - g)(x) = -5x + 25 \][/tex]

From the given choices, the correct answer is:
[tex]\[ (f - g)(x) = -5x + 25 \][/tex]

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