Question

Rental A is C=30x +50
Rental B is C =70x+40
The customer used substitution to find when the cost would be the same

Answer 1

To determine when the costs of Rental A and Rental B are equal, you can set the equations for the two rentals equal to each other and solve for \( x \).

The equations are:

1. \( C_A = 30x + 50 \) (Rental A)
2. \( C_B = 70x + 40 \) (Rental B)

Setting the two equations equal to each other:

\[
30x + 50 = 70x + 40
\]

Now, let's solve for \( x \):

1. Subtract \( 30x \) from both sides:

\[
50 = 40 + 40x
\]

2. Subtract 40 from both sides:

\[
10 = 40x
\]

3. Divide by 40:

\[
x = \frac{10}{40} = \frac{1}{4}
\]

Now that we have \( x = \frac{1}{4} \), we can substitute this back into either equation to find the cost at this point. Let's use Rental A:

\[
C_A = 30\left(\frac{1}{4}\right) + 50 = 7.5 + 50 = 57.5
\]

Thus, both Rental A and Rental B would have a cost of $57.5 when \( x = \frac{1}{4} \).

So, the costs are equal at:

\[
x = \frac{1}{4} \quad \text{with a cost of} \quad C = 57.5.
\]