Question

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?

Answer 1

x = 12

y = 22

Total amount = $2596

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