A person invests $5000 in treasury notes and bonds. The notes pay 8% annual interest and the bonds pay 10% annual interest. If the annual in- come is $480, how much is invested in treasury notes?

Investment in treasury notes is ##$1000##.

Let the money invested in treasury notes be ##$x##. Annual income on it at ##8%## per annum for a year will be ##8/100 xx x##.

Then money invested in bonds at ##10%## would be ##$(5000-x)## and annual income on it for a year will be ##10/100 xx (5000-x)##.

As total yield is ##480##, we have

##(8x)/100+(10(5000-x))/100=480## - multiplying both sides by ##100##

or ##8x+10(5000-x)=48000##

or ##8x+50000-10x=48000##

or ##-2x=48000-50000=-2000##

i.e. ##x=-2000/-2=1000##

Hence, investment in treasury notes is ##$1000##.