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?

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"



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



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):



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

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