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19 September, 20:28

jose invests money in two simple interests account. he invests twice as much in an account paying 13% as he does in an account paying 5%. if he earns $93.00 in interest in one year from both accounts combined how much did he invest altogether

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  1. 19 September, 20:32
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    He invested altogether $900

    Step-by-step explanation:

    * Lets explain how to solve the problem

    - Jose invests money in two simple interests account

    - He invests twice as much in an account paying 13% as he does in

    an account paying 5%

    - That means the amount he invested in the account paying 13% is

    twice the amount he invested in the account paying 5%

    - He earns $93.00 in interest in one year from both accounts combined

    - We need to find how much he invested in each account

    - Assume that he invested $x in the account paying 5%

    ∵ He invested twice as much in an account paying 13% as he does in

    an account paying 5%

    ∴ He invested $2x in the account paying 13%

    - The simple interest I = PRT, where P is the money invested, R is the

    rate of interest in decimal and t is the time of investment

    # Account paying 13%

    ∵ P = 2x, R = 13/100 = 0.13, T = 1

    ∴ I = 2x (0.13) (1)

    ∴ I = 0.26 x ⇒ (1)

    # Account paying 5%

    ∵ P = x, R = 5/100 = 0.05, T = 1

    ∴ I = x (0.05) (1)

    ∴ I = 0.05 x ⇒ (2)

    ∵ He earns $93.00 in interest in one year from both accounts

    - Add (1) and (2) and equate the sum by 93.00

    ∴ 0.26 x + 0.05 x = 93.00

    - Add like terms in the left hand side

    ∴ 0.31 x = 93.00

    - Divide both sides by 0.31

    ∴ x = 300

    ∴ 2x = 2 (300)

    ∴ 2x = 600

    ∵ x represents the amount of money invested in the account paying 5%

    ∴ The amount of money invested in the account of 5% is $300

    ∴ The amount of money invested in the account of 13% is $600

    - The total amount of money he invested is the sum of the money

    he invested in each account [$300 + $600 = $900]

    ∴ He invested altogether $900
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