Question

Mia borrowed some money from her friend in order to help buy a new video game system. Mia agreed to pay back her friend $8 per week and originally borrowed $80. Write an equation for L, in terms of t, representing the amount Mia owes her friend after t weeks.

Answer 1

Answer:

$L = 80 - 8t$

Step-by-step explanation:

Given

$Debt = \ 80$

$Weekly\ Payment = \ 8$

Required

Write an equation to determine the payment at a given week

At week 1, she'd have paid $8

At week 2, $16

Week 3, $24

..

.

This leads to arithmetic progression (AP):

8, 16, 24.....

To further solve, we'll make use of AP formula

$T_n = a + (n - 1)d$

In this case;

$t = n$

$d = 16 - 8 = 24 - 16 = 8$

$a = 8$

So, the equation becomes

$T_n = 8 + (t - 1) * 8$

$T_n = 8 + 8t - 8$

Collect Like Terms

$T_n = 8t + 8 - 8$

$T_n = 8t$

The above represents the amount paid at a particular week;

Amount owed, L is then calculated as follows;

$L + T_n = 80$

$L = 80 - T_n$

$L = 80 - 8t$