Kenya plans to make a down payment plus monthly payments in order to buy a motorcycle. at one dealer she would pay $2,250 down and $175 each month. at another dealer, she would pay $2,850 down and $150 each month. after how many months would the total amount paid be the same for both dealers? what would that amount be?

We use X to represent the number of months involved. In the first scenario, the expression for the amount paid is 2250 + 175X. In the second, the expression is 2850 + 150X. We set them equal to each other, because we want to know when the amount paid is the same. 2250 + 175X = 2850 + 150X. We move like to like and get 2850 - 2250 = 175X - 150X. This leaves 25X = 600, and so X = 600/25 = 24. It would take 24 months for this to happen, and subbing back in, the amount is 2250 + 175(24) = 6450.