Question

Aaron needs to take out a loan to purchase a motorcycle. At one bank, he would pay $2500 initially and $150 each month for the loan. At another bank, he would pay $3000 initially and $125 each month. After how many months will the loan payments be the same?

Answer 1

Hi
3000+125x=2500+150x
500=25x
x=500/25
x=20
Therefore the answer will be 20 months.
All the best!

Answer 2

20 months

Explanation:

Let x represent the number of months.

We have been given that at one bank, Aaron would pay $2500 initially and $150 each month for the loan. So amount paid in x months would be
`150x+2500`.

We are also told that at another bank, Aaron would pay $3000 initially and $125 each month for the loan. So amount paid in x months would be
`125x+3000`.

To find the number of months when both loan payments will be the same, we will equate both expressions as:

`150x+2500=125x+3000`

`150x-125x+2500=125x-125x+3000`

`25x+2500=3000`

`25x+2500-2500=3000-2500`

`25x=500`

`(25x)/(25)=(500)/(25)`

`x=20`

Therefore, after 20 months both loan payments would be the same.