Question

Kenya plans to make a down payment plus monthly payment in order to buy a motorcycle. At one dealer she would pay $2,500 down and $150 each month. At another dealer, she would pay $3,000 down and $125 each month. After how many month would the total amount paid be the same for both dealers? What would that the amount be?

Answer 1

First, create an equation for the price of the car for both dealerships:

Dealership A: y = 150x + 2500
Dealership B: y = 125x + 3000

where y is the total cost of the car and x is the number of months that have passed.

You know that y is equal to "150x + 2500" AND y is equal to "125x + 3000," so "150x + 2500" must be equal to "125x + 3000"


`150x+2500=125x+3000`

Now, just solve for x to find the number of months at which the total amount paid would be the same for both dealers:


`150x+2500=125x+3000\\150x-125x+2500=3000\\25x+2500=3000\\25x=3000-2500\\25x=500\\25x/25=500/25\\x=20`

So, after 20 months, the price of the car at both dealerships is the same. To find that price, just plug in 20 for x in one of the equations (because x was the number of months):


`y=150x+2500\\y=150(20)=2500\\y=3000+2500\\y=5500`

So, the car costs the same after 20 months, $5500 at either dealership.