linear systems help?

Question

An investor has $59,000 to invest in three types of bonds. They are short term, intermediate term, and long term. How much should she invest in each type to satisfy the given conditions? Short term bonds pay 4% annually, intermediate term bonds pay 6%, and long term bonds pay 8%. The investor wishes to have a total annual return of $3,800 on her investment, with equal amounts invested in intermediate term and long term bonds.

Answer 1

Let each bond be the x, y, and z (the variables) of the system. Since y = z, then the short term would be x, the intermediate term would be y, and the long term would be y. These bonds add up to $59,000:

x + y + y = 59,000

Then, the short term bond will pay 4%, the intermediate term will pay 6%, and the long term will pay 8%. The total payout will be:

0.04x + 0.06y + 0.08y = 3800

The system will be::
1) x + 2y = 59,000
2) 0.04x + 0.14y = 3800

Multply equation 2 by 25 and subtract that from equation 1. This is to cancel out the x's:
....x + 2y = 59000
.- (x+3.5y = 95000)
----------------------------
You get: -1.5y = -36000 ==> 1.5y = 36000 ==> y = 24,000

From here, you get x = 11,000.

ANSWERS:
Short term - $11,000
Intermediate Term - $24,000
Long Term - $24,000

Answer 2

You should solve these two equations.
x+2y=59000
x*4%*1+y*%6*1+y*%8*1=3800

x=?
y=?