Question

Samantha has found a great deal on an acoustic guitar, but she doesn’t have enough money saved up to buy it. She convinces her parents to loan her $150 so that she can buy it. At the end of each week that Samantha has not paid back the loan, she has to add $3 to how much she owes her parents. If she is able to save up enough money to pay her parents back $20 each week, which of the following expressions correctly represents how much she will still owe her parents after t weeks?

Answer 1

To find out how much Samantha will still owe her parents after t weeks, we calculate the initial loan amount plus the interest accrued for each week and then subtract what she has paid back. The expression for the remaining amount she will owe is $150 + $3t - $20t, which simplifies to $150 - $17t.

Step-by-step explanation:

Since Samantha owes her parents $150 initially and adds $3 to the amount she owes each week, we can say that after t weeks, without making any payments, she would owe $150 + $3t. However, she is able to pay back $20 each week. Therefore, the amount she pays back after t weeks is 20t.

To represent how much Samantha will still owe her parents after t weeks, we need to start with the initial loan amount, add the interest that accumulates for t weeks, and subtract the amount she has been able to pay off over t weeks. Therefore, the expression is:

(Initial Amount) + (Interest Accrued) - (Amount Paid Back) =

$150 + ($3 x t) - ($20 x t)

The simplified expression representing how much Samantha will still owe her parents after t weeks is:

$150 + $3t - $20t.

Fully simplifying this expression, we get:

$150 - $17t.