The statement recalls Fibonacci sequence.
In Fibonacci sequence, the first two numbers are 0 and 1, and from there the numbers are the sum of previous two numbers, so the series is:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 ...
As you see the first two numbers are fixed and the next are calculated witht the rule of the addition of the two previous numbers.
The problem sayt that the since 7 years ago the prices followed the rule of being the sum of the prices of the two years before.
We are in year 7, and know that in year 6 the price was 60c.
So, next year (year 8) the price will be 60 + price in year 7
year 8 = year7 + year6 = year7 + 60
and you can go backward.
year7 = year6 + year 5 = 60 + year5
year6 = year5 + year4 = 60
year5 = year4+year3
year4 = year3 + year2
year3 = year2 + year1
Before that you need to make an assumption.
Was the price before the year 1 constant or they were as per the two first numbers of Fibonacci series, which are 0 and 1?.
We just know how the prices skyrocketed since year 1.
I will make the problem in two ways:
First approach: year 1's price = x and previos year price = 0
year price
1 x
2 x+ 0 = x
3 x+x =2x
4 2x+x = 3x
5 3x+2x = 5x
6 5x+3x =8x
In that year the price is 60 c.
Then, 8x = 60 => x = 60/8 = 7.5 c
=> Price next year = 8x + 5x = 13x = 13(7.5) = 97.5 c
=> Price seven years ago = x = 7.5 c
Second approach: year's 1 price = x and two prices in the two previous years are 0 and 1
year price
1 x
2 x+1
3 2x+1
4 3x+2
5 5x + 3
6 8x + 5
Then 8x + 5 = 60 => 8x = 55 => x = 55/8 = 6.875
=> price next year = 13x + 8 = 13(6.875) + 8 = 97.375
=> price year 1 - 6.875
There is not practical difference between the two assumptions, but the statement should be clear regarding all the information and that include how are the prices before seven years ago to calculate the prices in the two first years of the last seven years.
