Final answer:
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.