Question

A boat dealership offers interest-free boat loans for one day only. During this day, a salesperson at the dealership sells two boats. Tom decides to pay off a $16,848 boat in 36 monthly payments of $468. Sandra decides to pay off a $13,560 boat in 60 payments of $226.

Write the system of linear equations.

When will the payoff amount be the same?
How much is left to pay off each boat?

Answer 1

Tom will take approximately 36 months to pay off the boat, while Sandra will take approximately 60 months. The payoff amount will be the same for both after approximately 36 and 60 months. There will be no amount left to pay off for both Tom and Sandra by the end of their payment periods.

Step-by-step explanation:

Let x represent the number of months it takes to pay off the $16,848 boat for Tom.

The equation for Tom's monthly payments can be written as:

468x = 16,848

Simplifying the equation, we get:

x = 16,848 / 468

x ≈ 36

Therefore, it takes Tom approximately 36 months to pay off the boat.

Now, let y represent the number of months it takes to pay off the $13,560 boat for Sandra.

The equation for Sandra's monthly payments can be written as:

226y = 13,560

Simplifying the equation, we get:

y = 13,560 / 226

y ≈ 60

Therefore, it takes Sandra approximately 60 months to pay off the boat.

The payoff amount will be the same when x and y are equal:

x = y

16,848 / 468 = 13,560 / 226

36 ≈ 60

Therefore, the payoff amount will be the same after approximately 36 and 60 months for Tom and Sandra, respectively.

To calculate the amount left to pay off each boat, we can subtract the total amount paid from the original amount:

For Tom:

Amount left to pay off = $16,848 - ($468 * 36)

For Sandra:

Amount left to pay off = $13,560 - ($226 * 60)

Performing the calculations, we get:

Amount left to pay off for Tom ≈ $0

Amount left to pay off for Sandra ≈ $0