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20 February, 14:21

A rich woman deposits a whole number of dollars x in her bank. The next time she deposits y dollars (still a whole number). Each subsequent deposit is the sum of the two previous deposits. Her 5th deposit was only $90, but her 10th deposit is exactly one thousand dollars. Find x and y first, then answer the question. Show your work.

What is the total amount of money in the bank?

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  1. 20 February, 15:40
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    x = 12

    y = 22

    Total amount = $2596

    Step-by-step explanation:

    First let's find the value of each deposit until the 10th in relation to x and y:

    1st: x

    2nd: y

    3rd: x + y

    4th: x + 2y

    5th: 2x + 3y

    6th: 3x + 5y

    7th: 5x + 8y

    8th: 8x + 13y

    9th: 13x + 21y

    10th: 21x + 34y

    Now, we can write a system with two equations and two variables:

    2x + 3y = 90

    21x + 34y = 1000

    From the first equation: x = (90 - 3y) / 2

    Using this value of x in the second equation, we have:

    21 * (90 - 3y) / 2 + 34y = 1000

    945 - 31.5y + 34y = 1000

    2.5y = 55

    y = 22

    Now we can find x:

    x = (90 - 3*22) / 2 = 12

    Now, summing all the deposits, we have a total of 55x + 88y, which is equal to 55*12 + 88*22 = $2596
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