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?

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Question:

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?

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Answer:The principal for the first account is $5000The principal for second account is $4600Step-by-step explanation:The formula for simple interest is expressed as I = PRT/100Where P = principalT = time in yearsR = interest rate on the principal.Let x represent the amount invested in the first accountLet y represent the amount invested in the second accountGabriel invests $9600 in two different accounts. This means that x + y = 9600 - - - - - - - -1For first account, The interest rate is 13%. The duration is one year.ThereforeP = xT = 1 yearR = 13%ThereforeI = (x × 13 × 1)/100I = 0.13xFor second account, he interest rate is 6%. The duration is one year.Let y represent the principal for the second account. ThereforeP = yT = 1 yearR = 6ThereforeI = (y × 6 × 1)/100I = 0.06yAt the end of the first year he had earned $926 in interest. This means that0.13x + 0.06y = 926 - - - - - - - -2Substituting x = 9600 - y into equation 2, it becomes0.13(9600 - y) + 0.06y = 9261248 - 0.13y + 0.06y = 926 - 0.13y + 0.06y = 926 - 1248- 0.07y = -322y = - 322/- 0.07 = 4600x = 9600 - y x = 9600 - 4600x = 5000

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