Phyllis invested 42000 dollars, a portion earning a simple interest rate of
4 percent per year and the rest earning a rate of 7 percent per year. After one year the total interest earned on these investments was 2220 dollars. How much money did she invest at each rate?
DONT SAY I DONT KNOW

Answers:

Work Shown:

x = amount invested at 4%

If she invests x dollars at 4%, then the rest (42000-x) must be invested at the other rate of 7%

She earns 0.04x dollars from that first account and 0.07(42000-x) dollars from the second account

This means we have

0.04x+0.07(42000-x)

0.04x+0.07*42000-0.07x

0.04x+2940-0.07x

-0.03x+2940

This represents the total amount of money earned after 1 year.

We're told the amount earned in interest is $2220, so we can say,

-0.03x+2940 = 2220

-0.03x = 2220-2940

-0.03x = -720

x = -720/(-0.03)

x = 24000 dollars is the amount invested at 4%

42000-x = 42000-24000 = 18000 dollars was invested at 7%

As a check, we can see that

18000+24000 = 42000

and also

0.04x = 0.04*24000 = 960 earned from the first account

0.07*18000 = 1260 earned from the second account

1260+960 = 2220 is the total interest earned from both accounts combined

This confirms our answers.

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