Question 694590: Jack has $10,000 to invest in three accounts. He invests part of the money at 7% annual interest and twice that amount in an account paying 5.5% annual interest. The remaining money is invested at 4% annual interest. How much was invested in Each account if the total annual income from the three investments was $490?
I tried the question and got it wrong. I did:
.07x+5.5(2x)=490
.07x+11x=490
11.07x=490
x=44.26
4y=10000
y=2500
$44.26=7%
$88.52=5.5%
$2500=4%
Found 2 solutions by mananth, MathTherapy:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! 7.5% ------------->x
5.5%---------------->2x
Balance amount = (10000-(x+2x))
(10000-(x+2x))-----------> 4%
Sm up individual interests
7%x+5.5%*2x+(10000-(x+2x))*4%=49000
multiply equation by 100
7x+11x+40000-12x=49000
6x=9000
x= 9000/6
x= 1500 amount invested at 7%
2x= 3000 amount at 5%
Balance 5500 at 4%
CHECK
1500 7.00% 105
3000 5.50% 165
5500 4.00% 220
490
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! Jack has $10,000 to invest in three accounts. He invests part of the money at 7% annual interest and twice that amount in an account paying 5.5% annual interest. The remaining money is invested at 4% annual interest. How much was invested in Each account if the total annual income from the three investments was $490?
I tried the question and got it wrong. I did:
.07x+5.5(2x)=490
.07x+11x=490
11.07x=490
x=44.26
4y=10000
y=2500
$44.26=7%
$88.52=5.5%
$2500=4%
Sorry to say but you're way off!!
Let amount invested in the 7% and 4% interest-accounts be S, and F, respectively
Amount he invested in account paying 5.5% = 2S
Therefore, S + F + 2S = 10,000 ---- 3S + F = 10,000 ----- eq (i)
Also, .07S + .055(2S) + .04(F) = 490 --- .07S + .11S + .04F = 490 --- .18S + .04F = 490 --- eq (ii)
- .12S - .04F = - 400 ------ Multiplying eq (i) by - .04
.06S = 90 ---- Adding eqs (ii) & (i)
S, or amount invested in the  % interest-account =  , or $
Amount invested in the  % interest-account = 2(1,500), or $
3(1,500) + F = 10,000 ------ Substituting 1,500 for S in eq (i)
4,500 + F = 10,000
F, or amount invested in the  % interest-account = 10,000 – 4,500, or $
You can do the check!!
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