Please show the work/explain. I need to write it down. Kenya plans to make a down payment plus monthly payments in order to buy a motorcycle. At one dealer she Kenya plans to make a down payment plus monthly payments 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 months would the total amount paid be the same for both
dealers? What would that amount be?

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Step-by-step explanation:

There are a couple of ways to work a problem like this. You have probably been taught to write equations for each of the payment amounts as a function of time, then equate those values to solve for the time that makes them equal.

  at dealer 1, the total amount paid (y) will be a function of months (x):

     y = 2500 +150x

  at dealer 2, the corresponding equation is ...

     y = 3000 +125x

These are equal when ...

  y = y

  2500 +150x = 3000 +125x

  25x = 500 . . . . . . . . . subtract 125x +2500 from both sides

  x = 500/25 = 20

The total paid will be the same after 20 months.

That amount is ...

  y = 2500 +150(20) = 5500

$5500 will be paid to either dealer after 20 months.

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The other way to work the problem is to "cut to the chase". The difference in down payment is made up at the rate of difference in monthly payments. So The number of monthly payments (x) required to equal the difference in down payments is ...

  25x = 500 . . . . . . . . . you may recognize this equation from above

  x = 500/25 = 20

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