Question

A forest has 5040 trees.

The trees are beech or maple.
number of beech : number of maple = 3.2 : 1
What fraction of the trees are beech?
Give your answer as a fraction in its simplest form.

Answer 1

3/5

Explanation:

Let the number of beech trees be 3x and the number of maple trees be 2x (since the ratio of beech to maple is 3.2 : 1, we can choose any common factor for the numbers of beech and maple trees).

So, the total number of trees is 3x + 2x = 5x.

We are given that the total number of trees is 5040, so:

5x = 5040

x = 1008

Therefore, the number of beech trees is 3x = 3(1008) = 3024, and the number of maple trees is 2x = 2(1008) = 2016.

The fraction of trees that are beech is:

3024 / (3024 + 2016) = 3024 / 5040

To simplify this fraction, we can divide both the numerator and denominator by their greatest common factor, which is 1008:

3024 / 5040 = (3024 ÷ 1008) / (5040 ÷ 1008) = 3 / 5

Therefore, the fraction of trees that are beech is 3/5.