Two rental car agencies have different rates for their minivans for one day. Car company A: has a flat fee of $35 and 25 cents per mile. Car company B: has a flat fee of $40 and 20 cents per mile.

Algebraically determine the number of miles that the two companies will charge the same.

First is to make equations for both sides.

Let x be the number of the miles.

a be the charge of the first company

b be the charge of the second

a=$35+$0.25 (x), b=$40+$0.20 (x).

then a=b

Substitute the equations

$35+$0.25 (x) = $40+$0.20 (x)

$0.25x - $0.20x = $40 - $35

$0.05x = $5

x = $5/$0.05, cancel out the unit.

x = 100

To justify substitute x to both the equations a and b.

a = 35 + 0.25 (x)

a = 35 + 0.25 (100)

a = 35 + 25

a = $60

b = 40 + 0.20 (x)

b = 40 + 0.20 (100)

b = 40 + 20

b = 60

a=b

60=60.