Question

Loan Mixture: A student takes out a total of $5000 in three loans: one subsidized, one unsubsidized, and one from the parents of the student. The subsidized loan is $200 more than the combined total of the unsubsidized and parent loans. The unsubsidized loan is twice the amount of the parent loan. Find the amount of each loan.

Step 1:

x = subsidized
y = unsubsidized
z = parent

Step 2:

x + y+ z = 5000

Step 3:




Solution:

Subsidized loan =
Unsubsidized loan =
Parent loan =

Answer 1

Get everything in terms of one variable
If the parent loan is Z
the unsubsidized loan is 2Z
the subsidized loan is 200 + Z + 2Z
5000=Z + 2Z + 200 + Z +2Z solve for Z
5000=6Z + 200
4800=6Z
800=Z
The parent loan is 800
The unsubsidized loan is 1600
The subsidized loan is 2600