Question

A $9,000 principal is invested in two accounts, one earning 7% interest and another earning 9% interest. If the total interest for the year is $782, then how much is invested in each account?

Answer 1

Answer:

The amount invested at 7% is $1,400 and the  amount invested at 9% is $7,600

Step-by-step explanation:

Let

x ----> amount invested at 7%

(9,000-x) -----> amount invested at 9%

we know that

The interest earned by the amount invested at 7% plus the interest earned by the amount invested at 9% must be equal to $782

so

The linear equation that represent this problem is

$0.07(x)+0.09(9,000-x)=782$

solve for x

$0.07x+810-0.09x=782\\0.09x-0.07x=810-782\\0.02x=28\\x=\ 1,400$

$(9,000-x)=9,000-1,400=\ 7,600$

therefore

The amount invested at 7% is $1,400 and the  amount invested at 9% is $7,600