You are moving across town and need a moving truck. At Moove-Ing you can rent a truck for $30

Question

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.