Question

Morgan invested $4,200 into two accounts. One account paid 4% interest and the other paid 7.5% interest. She earned 7% interest on the total investment. How much money did she put in each account?

Answer 1

The amount invested at 4% was $600

The amount invested at 7.5% was $3,600

Explanation:

Let

x ----> the amount invested at 4%

$4,200-x -----> amount invested at 7.5%

we know that

The total interest earned is equal to the interest earned by the amount invested at 4% plus the interest earned by the amount invested at 7.5%

Remember that

`4\%=4/100=0.04`

`7.5\%=7.5/100=0.075`

`7\%=7/100=0.07`

so

The linear equation that represent this situation is

`0.04x+0.075(4,200-x)=0.07(4,200)`

Solve for x

`0.04x+315-0.075x=294`

`0.075x-0.04x=315-294`

`0.035x=21`

`x=\$600`

`\$4,200-x=\$3,600`

therefore

The amount invested at 4% was $600

The amount invested at 7.5% was $3,600