Answer provided below:
Ms. Jones purchased a total of $45,000 in stocks, bonds, and money
market funds. The total she invested in bonds and money market funds
was twice the amount she invested in stocks. The return rates on the
stocks, bonds, and money market funds were 10.0%, 7.0%, and 7.5%
respectively. The total value of the return was $3,660. How much of
each investment (stock, bonds, and money market funds) did Ms Jones
purchase?
X=Stocks
Y=Bonds
Z=Money market funds
X+Y+Z=45000
Y+Z=2X
0.10X+0.07Y+0.075Z=3660
3X=45000
X=15000
Y+Z=30000
0.07Y+0.075Z=3600-0.1(15000)=2160 <== Should be: 0.07Y+0.075Z=3660-0.1(15000)=2160
Answer:
You've made a good start in setting this problem up, correctly solving for X.
X = 15000
The solution for Y and Z is achived as follows:
Y+Z=30000
Y = 30000 - Z
Substitute X=15000 and Y=30000-Z into your equation above: 0.10X+0.07Y+0.075Z=3660
0.10(15000) + 0.07(30000 - Z) + 0.075(Z) = 3660
1500 + 2100 - .07(Z) + .075(Z) = 3660
3600 + .005(Z) = 3660
.005(Z) = 60
5Z = 60000
Z= 12000
Substituting Z into Y = 30000 - Z
Y = 30000 - 12000
Y = 18000
In summary
$15,000 invested in Stocks yielding $1,500 (10.0%)
$18,000 invested in bonds yielding $1,260 ( 7.0%)
$12,000 invested in money market yielding $ 900 ( 7.5%) |
