Question 169808: The problem:
Write a system of equations to solve the following problem. Be sure to identify what the variables represent. Then find the solution.
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 (stocks, bonds, and money market funds) did Ms. Jones purchase?
My attempt:
2x + 2x + x = 45000 (x = stocks with 2x = bonds and money market funds which are twice the amount of stocks)
x(10%) + x(7%) + x(7.5%) =3600
Solving the first equation I get: 5x = 4500; x = 9000
plug the value for x back into the equation and it adds up. ( 5 * 9000= 45000)
Insert the values of x into the second equation and it does not add up.
(9000 * 10%) + (18000 * 7%) + (18000 * 7.5) = 3510
The answer is off by $150 (3660 - 3510 = 150)
Am I reading this word problem wrong?
Found 3 solutions by stanbon, solver91311, gonzo:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Write a system of equations to solve the following problem. Be sure to identify what the variables represent. Then find the solution.
Ms. Jones purchased a total of $45,000 in stocks, bonds, and money market funds.
Value Equation: s + b + m = 45000
-------------------------------------
The total she invested in bonds and money market funds was twice the amount she invested in stocks.
Value Equation: b+m = 2s
or 2s - b -m = 0
-------------------------------------
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.
Interest Equation: 0.10s + 0.07b + 0.075m = 3600
or 10s + 7b + 75m = 360000
-------------------------------------
How much of each investment (stocks, bonds, and money market funds) did Ms. Jones purchase?
------
You have 3 equations with three variables:
s + b + m = 45000
2s - b - m = 0
10s + 7b + 75m = 360000
-------------------------
Solve using any system you know to get:
s = 15000
b = 30000
m = 0000
=============
Cheers,
Stan H.
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website! Yep.
The total invested in bonds AND money market is twice the amound in stocks, so if x represents the amount invested in stocks, then 2x represents the amount invested in both bonds AND money market funds, therefore:
 is the correct first equation. Solving,  , so the total invested in stocks was $15,000 and the total invested in bonds AND money market was $30,000.
That means that the total return with respect to stocks was 10% of 15,000 or $1500. It also means that the total return with respect to bonds AND money market funds was $3,660 - $1,500 or $2,160.
Let's now say that the amount invested in bonds is b and the amount invested in the money market is m.
We know two things:
 and
Rearranging the first equation we get  and then substituting in the second equation we get:
Now simply solve for b and then subtract the value of b from 30000 to get m.
Hope that helps.
Answer by gonzo(654) (Show Source):
You can put this solution on YOUR website! here's how i solved it:
let s = stocks
let b = bonds
let m = money market funds
-----
s + b + m = 45000
.10*s + .07*b + .075*m = 3660
-----
"The total she invested in bonds and money market funds was twice the amount she invested in stocks"
2s = (b+m)
divide both sides of equation by 2:
s = (b+m)/2
-----
i started off with 2 equations in 3 unknowns.
using the fact of s = (b+m)/2, i was able to substitute (b+m)/2 for s which created 2 equations in 2 unknowns.
-----
substituting (b+m)/2 for s in both equations gets:
(b+m)/2 + b + m = 45000
.10*(b+m)/2 + .07*b + .075*m = 3660
-----
multiplying both equations by 2 gets:
(b+m) + 2b + 2m = 90000
.10*(b+m) + .14*b + .15*m = 7320
-----
remove parentheses from both equations:
b + m + 2b + 2m = 90000
.10*b + .10*m + .14*b + .15*m = 7320
combine like terms:
3b + 3m = 90000
.24*b + .25*m = 7320
-----
multiply the second equation by 12. this makes 3m in both equations so the m can cancel out and we can solve for b.
-----
3b + 3m = 90000
2.88b + 3m = 87840
-----
subtract the second equation from the first equation:
.12b = 2160
divide boths sides of the equation by .12
-----
b = 2160/.12 = 18000
-----
substitute 18000 for b in the first equation after you combined like terms.
3b + 3m = 90000
3*18000 + 3m = 90000
54000 + 3m = 90000
subtract 54000 from both sides:
3m = 90000 - 54000 = 36000
divide both sides by 3:
m = 36000 / 3 = 12000
-----
you have so far:
b = 18000
m = 12000
solve for s by substituting in the original equation shown below:
s + b + m = 45000
s + 18000 + 12000 = 45000
combine like terms:
s + 30000 = 45000
subtract 30000 from both sides:
s = 45000 - 30000 = 15000
-----
you now have all three:
s = 15000
b = 18000
m = 12000
-----
substitute in the second original equation as shown below:
.10*s + .07*b + .075*m = 3660
.10*15000 + .07*18000 + .075*12000 = 3660
1500 + 1260 + 900 = 3660
3660 = 3660
second equation is true so values for s, b, and m are correct.
-----
s should = (b+m)/2
substitute to get:
15000 = (18000 + 12000)/2
15000 = 30000/2
15000 = 15000
-----
looks good.
-----
i suspect the following statement is where you went wrong.
start of statement:
2x + 2x + x = 45000 (x = stocks with 2x = bonds and money market funds which are twice the amount of stocks)
end of statement:
-----
|
|
|
