Answer:
[tex]L = 80 - 8t[/tex]
Step-by-step explanation:
Given
[tex]Debt = \$80[/tex]
[tex]Weekly\ Payment = \$8[/tex]
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
[tex]T_n = a + (n - 1)d[/tex]
In this case;
[tex]t = n[/tex]
[tex]d = 16 - 8 = 24 - 16 = 8[/tex]
[tex]a = 8[/tex]
So, the equation becomes
[tex]T_n = 8 + (t - 1) * 8[/tex]
[tex]T_n = 8 + 8t - 8[/tex]
Collect Like Terms
[tex]T_n = 8t + 8 - 8[/tex]
[tex]T_n = 8t[/tex]
The above represents the amount paid at a particular week;
Amount owed, L is then calculated as follows;
[tex]L + T_n = 80[/tex]
[tex]L = 80 - T_n[/tex]
[tex]L = 80 - 8t[/tex]
