Question

A man invested one-third of his money at 5%, half of his money at 3%, and the rest at 4.5%. If his total annual investment income was $470, how much had he invested?

Answer 1

`\$12,000`

Explanation:

Let

x ----> the total amount of money to be invested

x/3 ----> amount of money invested at 5%

x/2 ----> amount of money invested at 3%

The rest of the money is x-(x/2 + x/3)=x/6

x/6 ----> amount of money invested at 4.5%

we know that

The interest earned by the amount of money at 5% plus the interest earned by the amount of money at 3% plus the interest earned by the amount of money at 4.5% must be equal to $470

so

`(0.05)(x)/(3) +(0.03)(x)/(2)+(0.045)(x)/(6)=470`

Solve for x

Multiply by 6 both sides to remove the fraction

`0.10x +0.09x+0.045x=470`

`0.10x +0.09x+0.045x=2,820`

`0.235x=2,820`

`x=\$12,000`