Devon invested $8000 in three different mutual funds. A fund containing large cap stocks made 6.2% return in 1 years. A real estate fund lost 13.5% in 1 year, and a bond fund made 4.4% in 1 year. The amount invested in the large cap stock fund was twice the amount invested in the real estate fund. If Devon had a net return of $66 across all investments, how much did he invest in each fund?
So far I have this:
[A]= large cap fund
[B]= real estate fund
[C]= bond fund
so,
a+b+c= 8000
a+b=16,000
62a-135b+44c=66,000 My question is the second equation looks iffy. I know that the application read the amount invested in the large cap fund was twice the amount invested in the real estate fund, so I took the $8000 and multiplied it by 2. I know something is wrong, I just can't pin point it.
You said A, B, and C for the funds. These are not the same as a, b, and c. You need to be consistent. Let's go with a, b, and c.
a + b + c = 8,000 ---- This is CORRECT ------- eq (i)
a + b = 16,000 ------- This is incorrect, and should be: a = 2b ------ eq (ii)
62a - 135b + 44c = 66,000 ------ This is correct ------ eq (iii)
2b + b + c = 8,000 ----- Substituting 2b for a in eq (i)
3b + c = 8,000_______c = 8,000 - 3b ------- eq (iv)
62(2b) - 135b + 44(8,000 - 3b) = 66,000 ------ Substituting 2b for a, and 8,000 - 3b for c in eq (iii)
Now, just solve for b!
Then, substitute the value of b into eq (ii) to get the value of a
Last, substitute values of b and a into eq (i) to get the value of c. Voila, you're finally done!