Question

Kiera recently bought a used car from a relative, who agreed to let her pay for the car over time. She also borrowed money from her parents for a summer internship in Washington, D.C. She is paying off both loans in equal weekly payments. Use the information in the photos to determine how many weeks it takes for the balances of the loans to be the same.

Answer 1

Using Arithmetic progression, after $29$ weeks the balances of the loans to be the same.

Both the situations represent Arithmetic progression.

Case $1$:

$a=6500, d=-200$.

nth term of an A.P is

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

$a_n=6500+(n-1)(-200)...(i)$

Case $2$:

$a=1600, d=-25.$

nth term of an A.P is

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

$a_n=1600+(n-1)(-25)...(ii)$

From $(i)$ and$(ii)$

$6500+(n-1)(-200)=1600+(n-1)(-25)$

$6500-200n+200=1600-25n+25$

$6500+200-1600-25=-25n+200n$

$5075=175n$

$n=29$.

So, after $29$ weeks the balances of the loans to be the same.

Learn more about A.P here:

https://brainly.com/question/11972947?referrer=searchResults