Douglas invests money in two simple interest accounts. He invests three times as much in an account paying 14% as he does in an account payi

Question

Douglas invests money in two simple interest accounts. He invests three times as much in an account paying 14% as he does in an account paying 5%. If he earns $152.75 in interest in one year from both accounts combined, how much did he invest altogether?

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Remi 2 weeks 2022-01-12T11:31:29+00:00 2 Answers 0 views 0

Answers ( )

  1. Charlotte
    0
    2022-01-12T11:32:52+00:00

    Answer:

    Altogether, he invested $1300.

    Step-by-step explanation:

    This is a simple interest problem.

    The simple interest formula is given by:

    E = P*I*t

    In which E are the earnings, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

    He invests three times as much in an account paying 14% as he does in an account paying 5%.

    I am going to call the earnings from the account paying 14% E_{1} and the earnings from the account paying 5% E_{2}. The principals are P_1 and P_{2}, in which P_{1} = 3P_{2}.

    So

    E_{1} = P_{1}*0.14t

    E_{2} = P_{2}*0.05t

    He earns $152.75 in interest in one year from both accounts combined.

    This means that

    E_{1} + E_{2} = 152.75

    I am going to write E_{1} as a function of E_{2} and replace in the first equation, that of E_{1}.

    So

    E_{1} = 152.75 - E_{2}

    E_{1} = P_{1}*0.14t

    We also have that

    P_{1} = 3P_{2}

    So

    152.75 - E_{2} = 3*P_{2}*0.14t

    In which

    E_{2} = P_{2}*0.05t

    So

    152.75 - P_{2}*0.05t = 0.42P_{2}t

    His earnings are after 1 year, so t = 1

    152.75 - P_{2}*0.05 = 0.42P_{2}

    0.42P_{2} + P_{2}*0.05 = 152.75

    0.47P_{2} = 152.75

    P_{2} = \frac{152.75}{0.47}

    P_{2} = 325

    His smaller investment is 325.

    P_{1} = 3P_{2} = 3*325 = 975

    How much did he invest altogether?

    This is P_{1} + P_{2}

    P_{1} + P_{2} = 975 + 325 = 1300

    Altogether, he invested $1300.

    0
    2022-01-12T11:33:27+00:00

    Answer:

    Step-by-step explanation:

    Let x represent the amount invested in the account paying 14% interest.

    Let y represent the amount invested in the account paying 5% interest.

    He invests three times as much in an account paying 14% as he does in an account paying 5%. This means that

    x = 3y

    The formula for simple interest is expressed as

    I = (PRT)/100

    Considering the account earning 14% interest,

    I = (x × 14 × 1)/100 = 0.14x

    Considering the account earning 5% interest,

    I = (y × 5 × 1)/100 = 0.05y

    If he earns $152.75 in interest in one year from both accounts combined, it means that

    0.14x + 0.05y = 152.75 – – – – – – – – – -1

    Substituting x = 3y into equation 1, it becomes

    0.14(3y) + 0.05y = 152.75

    0.42y + 0.05y = 152.75

    0.47y = 152.75

    y = 152.75!0.47

    y = 325

    x = 3y = 3 × 325

    x = $975

    Total amount of money invested is

    975 + 325 = $1300

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