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?

Respuesta :

Answer:

The amount invested at 4% was $600

The amount invested at 7.5%  was $3,600

Step-by-step 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

[tex]4\%=4/100=0.04[/tex]

[tex]7.5\%=7.5/100=0.075[/tex]

[tex]7\%=7/100=0.07[/tex]

so

The linear equation that represent this situation is

[tex]0.04x+0.075(4,200-x)=0.07(4,200)[/tex]

Solve for x

[tex]0.04x+315-0.075x=294[/tex]

[tex]0.075x-0.04x=315-294[/tex]

[tex]0.035x=21[/tex]

[tex]x=\$600[/tex]

[tex]\$4,200-x=\$3,600[/tex]

therefore

The amount invested at 4% was $600

The amount invested at 7.5%  was $3,600

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