Question

A forest has 1260 trees.

The trees are maple, beech or oak.
A fifth of the trees are maple and the number of maple trees is 3 times the number of beech trees.
The rest of the trees are oak.
number of oak : number of beech = n : 1
Work out the value of n .
You must show how you get your answer.

Answer 1

`\huge\boxed{\sf n = 11}`

Explanation:

Total trees = 1260 trees

Maple trees:

`\displaystyle = (1)/(5) \ of \ total \ trees\\\\= (1)/(5) * \ 1260\\\\= (1260)/(5) \\\\= 252 \ maple \ trees`

Beech trees:

Given that:

Maple trees = 3 × beech trees

=> There are 252 maple trees.

252 = 3 × beech trees

Divide 3 to both sides

252 / 3 = beech trees

84 trees = beech trees

`\boxed{\sf beech \ trees = 84 \ trees\\}`

Oak trees:

It is said that all other trees are oak trees.

So, oak trees will be:

= total trees - maple trees - beech trees

= 1260 - 252 - 84

= 924 trees

The ratio of oak trees to beech trees:

= 924 : 84

Divide 84 to both sides

= 11 : 1

The question says:

number of oak : number of beech = n : 1

So, from the answer, it is clear that:

n = 11

`\rule[225]{225}{2}`