Question

A candy factory wants to compare a new machine to their current machine. Both machines produce y boxes of candy for every hour x. The current machine is represented by the equation f(x). The new machine is represented by the equation g(x).
f(x) = 15x + 90
g(x) = 30x + 30

After what number of hours will the amount of candy produced be the same for both machines?
Enter your answer in the box.

Answer 1

To find after how many hours the amount of candy produced by both machines will be the same, we need to set the equations \( f(x) \) and \( g(x) \) equal to each other.

The equations are:
- \( f(x) = 15x + 90 \)
- \( g(x) = 30x + 30 \)

Set them equal:
\[
15x + 90 = 30x + 30
\]

Now, we will solve for \( x \):

1. Subtract \( 15x \) from both sides:
\[
90 = 30x - 15x + 30
\]

This simplifies to:
\[
90 = 15x + 30
\]

2. Next, subtract 30 from both sides:
\[
90 - 30 = 15x
\]
\[
60 = 15x
\]

3. Finally, divide both sides by 15:
\[
x = \frac{60}{15}
\]
\[
x = 4
\]

Thus, after **4 hours**, the amount of candy produced by both machines will be the same.

The answer is \( \boxed{4} \).