Carol invested $2,560 into two accounts. One account paid 6% interest and the other paid 8% interest. She earned 7.25% interest on the total investment in one year. How much money did she put in each account? Use the general formula, I=Prt, to model simple interest applications, where I is equal to the interest, P is equal to the product of the principal, r is equal to the rate, and t is equal to the time.

The amount she put in the account that paid 6% interest = x = $960

The amount she put in the account that paid 8% interest = y = $1600

Step-by-step explanation:

Carol invested $2,560 into two accounts. One account paid 6% interest and the other paid 8% interest. She earned 7.25% interest on the total investment in one year.

I=Prt, to model simple interest applications, where I is equal to the interest, P is equal to the product of the principal, r is equal to the rate, and t is equal to the time.

Step 1

We have to calculate the total interest earn on the initial capital

P = $2,560

R = 7.25% = 0.0725

T = 1

I = $2,560 × 0.0725 × 1

I = $185.60

Let the amount Invested in the account that paid 6% interest = x

Let the amount Invested in the account that paid 8% interest = y

Hence:

$185.60 = x × 6% + y × 8%

$185.60 = 0.06x + 0.08yEquation 1

$2560 = x + y Equation.2

x = $2560 - y

$185.60 = 0.06x + 0.08yEquation 1

185.60 = 0.06(2560 - y) + 0.08y

185.60 = 153.6 - 0.06y + 0.08y

185.60 - 153.60 = 0.02y

y = 32/0.02

y = $1600

x = $2560 - y

x = $2560 - $1600

x = $960

The amount she put in the account that paid 6% interest = x = $960

The amount she put in the account that paid 8% interest = y = $1600