We have n dollars to spend Every day we buy either a candy f

We have n dollars to spend. Every day we buy either a candy for 1 dollar or an ice cream for 2 dollars. In how many ways can we spend the money?

Solution

Lets say Ice cream cost = 2$, Candy cost is =1$,

Lets assume some value of n

n= 2 ....2I+1C=2, we can buy 2 candy or 1 Ice cream......................2 ways

n=3......2I+1C=3, we can buy 3 Candy or 1 candy and 1 Ice cream...2 ways

n=8...2I+1c=8, we can buy

8Candy (or) 6 candy,1 Ice cream (or)4 candy,2 ice cream (or) 2 candy ,3 ice cream (or) 4 ice cream...5 ways

So we can generalise this as follows.

Ice cream co-efficient is 2 and Candy co-efficeint is 1, LCM of these two numbers is 2..

So total no of ways = Integer(n/LCM)+1 = Integer(n/2)+1

We need write the integer part when n/2 is fraction

e.g. If n=7 ... Answer will be = Integer(7/2)+1 = Integer(3.5)+1 = 3+1= 4 ways..

7 candy or 5 candy&1 ice cream (or) 3 candy & 2 ice cream (or) 1 candy & 3 ice cream