Question

In her last two years in college, Marlene received $42,000 in loans. The first year, she received a loan that was $6,000 less than three times the amount of the second year's loan. Call the amount that Marlene received her first year f and the amount she received in her second year s.

Answer 1

First year = 30000

Second year = 12000

Explanation:

Given

`Loan = \$42000`

Represent first year with f and second year with s.

So, we have:

`s + f = 42000`

and

`f = 3s - 6000`

Required

Solve for f and S

Substitute 3s - 6000 for f in the first equation.

`s + f = 42000`

`s + 3s - 6000 = 42000`

`4s - 6000 = 42000`

Collect Like Terms

`4s = 42000 + 6000`

`4s = 48000`

Solve for s

`s = 48000/4`

`s = 12000`

Substitute 12000 for s in
`f = 3s - 6000`

`f = 3 * 12000 - 6000`

`f = 36000 - 6000`

`f = 30000`