Kenya plans to make a down payment plus monthly payments in order to buy a motorcycle. At one dealer she would pay $2,350 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?

20 months

Step-by-step explanation:

Let x be the number of months. The cost equation for each dealer is the total of the down payment and the total monthly contribution. Thus,

Deal 1 cost = $2,350 + $175x

Dealer 2 cost = $2,850 + $150x

The number of months after which the costs from both dealers are equal is calculated by equating the costs for both dealers. Therefore,

$2,350 + $175x = $2,850 + $150x

$175x - $150x = $2,850 - $2,350

$25x = $500

x = $500/$25

x = 20 months