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?

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

Step-by-step explanation:

Let x represent the amount which he invested in the account earning 15% interest.

Let y represent the amount which he invested in the account earning 16% interest.

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

Considering the account earning 15% interest,

P = $x

T = 1 year

R = 15℅

I = (x × 15 × 1)/100 = 0.15x

Considering the account earning 16% interest,

P = $y

T = 1 year

R = 16℅

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

0.31x = 620

x = 620/0.31 = 2000

y = x + 1000 = 2000 + 1000

y = 3000

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