Question

4.7.5 stepping stones
joan has $75 to buy her friends a gift bag. the gift bags are $3 each. the function, $f(x) = -3x + 75$, represents the amount of money joan has left in her budget after purchasing $x$ gift bags.
complete the statements.
the solution for $f(x) = 0$ is $x = \square$ which $\square$ a viable solution in this scenario.

Explanation:

Step1: Set up the equation

We set \( f(x) = 0 \), so the equation is \( -3x + 75 = 0 \).

Step2: Solve for \( x \)

Subtract 75 from both sides: \( -3x = -75 \).
Divide both sides by -3: \( x=\frac{-75}{-3}=25 \).

Step3: Check viability

In this scenario, \( x \) represents the number of gift bags. Since 25 is a non - negative integer (you can buy 25 gift bags with $75 at $3 per bag), it is a viable solution.

Answer:

The solution for \( f(x) = 0 \) is \( x = 25 \), which is a viable solution in this scenario.