Last year, keiko had $20,000 to invest. she invested some of it in an account that paid %7 simple interest per year, and she invested the rest in an account that paid %5 simple interest per year. after one year, she received a total of $1,280 in interest. how much did she invest in each account?

Step-by-step explanation:

The formula of simple interest is:

Where I is the interest earned after t years

r is the interest rate

is the initial amount

We know that the investment was $20,000 in two accounts

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For the first account r = 0.07 per year.

Then the formula is:

Where

is the initial amount in account 1 at a rate during t = 1 year

For the second account r = 0.05 per year.

Then the formula is:

Where

is the initial amount in account 2 at a rate during t = 1 year

Then

We know that the final profit was I $1,280.

So

Substituting the values , and I we have:

As the total amount that was invested was $20,000 then

Then we multiply the second equation by -0.07 and add it to the first equation:

Then