Question

Miguel is renting a party bus for the prom. He can rent from Luxury Rentals for a $100 initial fee and then $2 a mile or from Slick Rentals for an initial fee of $20 and $10 per mile. After how many miles will the cost be the same? (Two variable systems)

Answer 1

To find when the cost of renting the party bus from Luxury Rentals and Slick Rentals will be the same, set up an equation using the costs of each company. After solving the equation, we find that the cost will be the same after 10 miles.

Step-by-step explanation:

To determine when the cost of renting the party bus from Luxury Rentals and Slick Rentals will be the same, we need to set up an equation. Let's assume that after x miles, the cost will be the same. The cost for Luxury Rentals can be expressed as $100 + $2x, and the cost for Slick Rentals can be expressed as $20 + $10x.

Setting the two costs equal to each other, we have:

$100 + $2x = $20 + $10x

Combining like terms, we get:

$2x - $10x = $20 - $100

$-8x = -$80

Dividing both sides by -8, we find that x = 10. Therefore, after 10 miles, the cost of renting from both companies will be the same.