Calculus Help Please
Mathematics

Tutor: None Selected  Time limit: 1 Day 
Yeartodate Loss  

SHPIX (Short Smallcap Profund)  6% 
RYURX (Rydex Inverse S&P 500)  5% 
RYIHX (Rydex Inverse High Yield)  7% 
You invested a total of $11,000 in the three funds at the beginning of 2011, including an equal amount in RYURX and RYIHX. Your yeartodate loss from the first two funds amounted to $450. How much did you invest in each of the three funds?
Thank you for the opportunity to help you with your question!
1) Write the equations. Let's set: x = Amount of money invested in SHPIX
y = Amount of money invested in RYURX
z = Amount of money invested in RYIHX
Since it was invested a total of $11,000 then our first equation is: x + y + z = 11,000
Then it says that it was invested the same amount in RYURX and RYIHX which means our second equation is: y = z
Finally, it says that yeartodate loss from the first two funds amounted to $450 (this comes from the interest of the first two investment). So its interest rate times its invested amount from the first two funds would be equal to the $450. So we have: 0.06x + 0.05y = 450
x + y + z = 11000
y = z
0.06x + 0.05y = 450
2) Then we solve the sytem of equations. Let's substitute the z by y into the first equation. So we have:
x + y + z = 11000 > x + y + y = 11000 > x + 2y = 11000
Now we solve for x in the last obtained equation.
x + 2y = 11000 > x + 2y  2y = 11000  2y > x = 11000  2y
Now we enter (11000  2y) in place of x into the equation: 0.06x + 0.05y = 450. So we have:
0.06(11000  2y) + 0.05y = 450 > 0.06*11000  0.06*2y + 0.05y = 450
660  0.12y + 0.05y = 450 > 660  0.07y = 450 > 660  660  0.07y = 450  660
0.07y = 210 > 0.07y/0.07 = 210/0.07 > y = $3000
Since y = z then z = $3000. And finally, we have:
x + y + z = 11000 > x + 3000 + 3000 = 11000 > x + 6000 = 11000
x + 6000  6000 = 11000  6000 > x = $5000
x = $5000 , y = $3000, z = $3000
Please let me know if you have any doubt or question :)
Thanks for taking the time to walk me through this problem. It did end up making much more sense once I saw the work.
Thanks Again!
Secure Information
Content will be erased after question is completed.