Carolyn received a check last week . She invested part at 15% and 1000 more than this amount at 16%. If she will earn $780 in interest in a year, how much was invested at each rate?

Somebody who is competent help me PLEASE

she invested $2000 at 15% and $3000 at 16%

Step-by-step explanation:

Let x represent the amount invested at 15%.

Let y represent the amount invested at 16%.

She invested part at 15% and 1000 more than this amount at 16%. This means that

y = x + 1000

The formula for determining simple interest is expressed as

I = PRT/100

Where

I represents interest paid on the amount invested.

P represents the principal or amount invested.

R represents interest rate

T represents the duration of the investment.

Considering the amount invested at 15%,

P = x

R = 15

T = 1

I = (x × 15 × 1)/100 = $0.15x

Considering the amount invested at 16%,

P = y

R = 16

T = 1

I = (y × 16 × 1)/100 = $0.16y

If she will earn $780 in interest in a year, it means that

0.15x + 0.16y = 780- - - - - - - - - - - - 1

Substituting y = x + 1000 into equation 1, it becomes

0.15x + 0.16(x + 1000) = 780

0.15x + 0.16x + 160 = 780

0.31x = 780 - 160 = 620

x = 620/0.31

x = 2000

y = x + 1000 = 2000 + 1000

y = 3000

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step-by-step explanation: