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Question
An amount is invested in bonds at 3 percent, real estate at 4 percent, and stocks at 5 percent.  The amount at 5 percent is half as much as the other two.

Income per year - $490

Total invested- $12,000

Calculate amount invested in each.

Answer
"An amount is invested in bonds at 3 percent, real estate at 4 percent, and stocks at 5 percent."
b, r, and s are the dollar amounts invested in bonds, real estate, and stocks, respectively.

"The amount at 5 percent is half as much as the other two."
This is ambiguous*. I think they mean "the amount at 5 percent is half THE SUM OF the other two."
s = (b+r)/2

"Total invested- $12,000"
b + r + s = 12,000
b + r + (b+r)/2 = 12,000
2b + 2r + (b+r) = 24,000
3b + 3r = 24,000
b+r = 8,000
r = 8,000-b
s = (b+r)/2 = (b+(8000-b))/2 = 4,000

"Income per year - $490"
0.03b + 0.04r + 0.05s = 490

substitution
0.03b + 0.04(8000-b) + 0.05(4,000) = 490
0.03b + 320 - 0.04b + 200 = 490
b = 3,000
r = 8,000-b = 5,000

$3,000 is invested in bonds at 3%
$5,000 is invested in real estate at 4%
$4,000 is invested in stocks at 5%
=====
*I first interpreted this as "the amount at 5 percent is half as much as the amount invested in either of the other two."
This would mean that s = b/2 = r/2, which in turn gives b=r=4,800 and s=2,400. This gives the wrong amount of interest income:
0.034,800 + 0.044,800 + 0.052,400 = $456

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