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Gabriel invests $9600 in two different accounts. The first account paid 13 %, the second account paid 6 % in interest. At the end of the first year he had earned $926 in interest. How much was in each account?

Respuesta :

Answer:The principal for the first account is $5000

The principal for second account is $4600

Step-by-step explanation:

The formula for simple interest is expressed as

I = PRT/100

Where

P = principal

T = time in years

R = interest rate on the principal.

Let x represent the amount invested in the first account

Let y represent the amount invested in the second account

Gabriel invests $9600 in two different accounts. This means that

x + y = 9600 - - - - - - - -1

For first account, The interest rate is 13%. The duration is one year.

Therefore

P = x

T = 1 year

R = 13%

Therefore

I = (x × 13 × 1)/100

I = 0.13x

For second account, he interest rate is 6%. The duration is one year.

Let y represent the principal for the second account. Therefore

P = y

T = 1 year

R = 6

Therefore

I = (y × 6 × 1)/100

I = 0.06y

At the end of the first year he had earned $926 in interest. This means that

0.13x + 0.06y = 926 - - - - - - - -2

Substituting x = 9600 - y into equation 2, it becomes

0.13(9600 - y) + 0.06y = 926

1248 - 0.13y + 0.06y = 926

- 0.13y + 0.06y = 926 - 1248

- 0.07y = -322

y = - 322/- 0.07 = 4600

x = 9600 - y

x = 9600 - 4600

x = 5000

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