Lakisha has a total of $8000 to invest in two accounts for 1 year. One pays 5% simple interest, and the other pays 6% simple interest. How much should she invest in each account so the total interest earned is $438?

Let the amount invested in the first account be x and let the amount invested in the second be 8000 - x

We have PRT/100 where P is her principal and r, her rate and t, the time

So in the first account I = x * 5 * 1/100

I = 5x/100

On the other hand if she gets 6% interest in the second account, we have I = PRT/100

So we have I = (8000 - x) * 6 * 1 / 100

I = (48000 - 6x) / 100

But the combined interst is 438 so we have

5x/100 + (48, 000 - 6x) / 100 = 438

Multiply through by 100

5x + 48, 000 - 6x = 43800

-x = 43800 - 48, 000

-x = - 4200

Hence x = 4200. She will have to invest 8000 - 4200 in the second account which is 3800

Simple interest rate is given by:

I = (PRT) / 100

let the amount invested in 5% S. I. be $x and amount invested in 6% S. I. be $ (8000-x)

Interest obtained from 5% will be:

I=5/100*1*x=0.05x

Interest obtained from 6% will be:

I=6/100*1 * (8000-x) = 0.06 (8000-x)

therefore total interest earned from the to schemes will be:

0.05x+0.06 (8000-x) = 438

solving for x we obtain:

0.05x+480-0.06x=438

0.05x-0.06x=438-480

-0.01x=-42

x=-42 / (-0.01)

x=$4200

hence amount invested in 5% S. I. is $4200 and amount invested in 6% S. I. is (8000-4200) = $3800