ms.smith invested 25000 in two accounts one yielding 4% interest the other 12%.If she received a total of 2280 in interest at the end of the

Question

ms.smith invested 25000 in two accounts one yielding 4% interest the other 12%.If she received a total of 2280 in interest at the end of the year how much did she invest in each account?

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Allison 4 weeks 2021-09-22T14:20:29+00:00 1 Answer 0

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    2021-09-22T14:21:32+00:00

    Answer: Ms Smith invested $9,000 in one account and $16,000 in the second account

    Step-by-step explanation:

    Now let us denote the amount she invested in the first account by “a” and denote the amount she invested in the second account by “b”.

    If she invested $25,000 in the 2 accounts, then:

    a + b = $25000 ——- call this equation (eqn)1

    Again, the first account yielded extra 4% of what was invested.

    Therefore 4/100 × a = 4a/100 (this is the amount the first account yielded)

    The second account yielded extra 12% of the invested amount

    Therefore 12%×b = 12b/100

    If the total sum of the interest the 2 accounts yielded was 2280, then:

    ( 4a/100) + (12b/100) = 2280 —–let this be eqn 2

    We now have simultaneous equations before us.

    In eqn 1, making b the subject of the formula:

    b = $25000 – a

    Substitute b for $25000 – a in eqn 2

    (4a/100) + [12(25000 – a)/100] = 2280

    300000 – 8a = 228000

    – 8a = 228000 – 300000

    a = -72000/-8

    a = $9000

    Now, we substitute “a” for $9,000 in eqn 1

    9000 + b = 25000

    b = 25000 – 9000

    b = $16,000

    So, Ms Smith invested separate sums of $9,000 and $16000 in the two accounts

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