Question

You are moving across town and need a moving truck. At Moove-Ing you can rent a truck for $30
a day with a one-time fee of $75
. At 2 Guy Movers, you can rent a truck for $25
a day with a one-time fee of $100
. Using substitution, find the number of days for which both rental companies would cost the same.

Answer 1

To find the number of days for which both rental companies would cost the same, we can set up equations based on the information given.

Let \( x \) be the number of days you rent the truck. The total cost for each company can be represented as follows:

1. **Moove-Ing:**
\[
\text{Cost}_1 = 30x + 75
\]

2. **2 Guy Movers:**
\[
\text{Cost}_2 = 25x + 100
\]

Next, we set the two equations equal to each other to find out when their costs are the same:

\[
30x + 75 = 25x + 100
\]

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

1. Subtract \( 25x \) from both sides:
\[
30x - 25x + 75 = 100
\]
\[
5x + 75 = 100
\]

2. Subtract 75 from both sides:
\[
5x = 100 - 75
\]
\[
5x = 25
\]

3. Divide by 5:
\[
x = \frac{25}{5}
\]
\[
x = 5
\]

Thus, the number of days for which both rental companies would cost the same is **5 days**.