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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?

Respuesta :

calculista

Answer:

[tex]\$12,000[/tex]

Step-by-step 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

[tex](0.05)\frac{x}{3} +(0.03)\frac{x}{2}+(0.045)\frac{x}{6}=470[/tex]

Solve for x

Multiply by 6 both sides to remove the fraction

[tex]0.10x +0.09x+0.045x=470[/tex]

[tex]0.10x +0.09x+0.045x=2,820[/tex]

[tex]0.235x=2,820[/tex]

[tex]x=\$12,000[/tex]

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