Question

Sam has a collection of stamps. He adds 4/5 of a new set of stamps to his collection. If his collection initially had 3/5 of the new set, what fraction of the new set does Sam have?

Answer 1

Sam has is 7/5 times the reciprocal of the total number of stamps in the new set.

Explanation:

Let's start by finding out what fraction of the new set of stamps Sam has after adding 4/5 of the set to his collection.

Let the total number of stamps in the new set be x.

If Sam's collection initially had 3/5 of the new set, then the number of stamps in his collection before adding the new set would be:

3/5 * x = the number of stamps in Sam's collection before adding the new set

After adding 4/5 of the new set to his collection, Sam has:

3/5 * x + 4/5 * x = 7/5 * x

So Sam has 7/5 of the new set of stamps.

However, the problem asks for the fraction of the new set that Sam has, not the fraction of the total number of stamps in the new set.

To find the fraction of the new set that Sam has, we need to divide the number of stamps he has by the total number of stamps in the new set:

(7/5 * x) / x

Simplifying the expression:

(7/5) / 1

We can express this fraction in terms of x by multiplying both the numerator and denominator by 1/x:

(7/5) * (1/x)

Therefore, the fraction of the new set of stamps that Sam has is 7/5 times the reciprocal of the total number of stamps in the new set.