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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.

"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%

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*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:

0.03·4,800 + 0.04·4,800 + 0.05·2,400 = $456

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