   SEARCH HOME Math Central Quandaries & Queries  Question from Mari, a parent: Cost of pencil is rising every year since 7 years ago. If the cost of pencil last year was 60 cents which is the sum of the cost from the last two previous years, what is the cost of the pencil now, the cost seven years ago. Mari,

I think the problem states that after the second year the cost each year is the sum of the costs in the two previous years.

Suppose the cost of a pencil in the first year is a cents and the cost in the second year is b cents then the cost in the third year is a + b cents and the cost in the fourth year is a + b + b = a + 2b cents. What is the cost of a pencil in the fifth year, the sixth year, the seventh year? You know the cost in the seventh year is 60 cents so equating the cost in the seventh year in terms of a and b to 60 cents gives an equation in a and b. Can you find integers a and b that solve this equation?

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.