Question

Shelley compared to the number of oak trees to the number of maple trees as part of study about hardwood trees in the world she counted nine maple trees into every oak tree later in the year there was a bug problem and many trees die new trees were planted to make sure there was a Stephen on the trees planted before the bug problem then you ratio of maple tree set a number of oak trees is 3 to 11 after planting new trees that were 132 Oak trees how many maple trees when the weather before the bug problem then after the problem

Answer 1

There were 36 more maple trees planted before the bug problem than after the bug problem.

Explanation:

Given:

Shelley counted 9 maple trees to every 5 oak trees.

The new ratio of maple trees to the oak trees is 3 to 11.

After planting new trees the total Oak trees were 132.

Now, to find the number of maple trees which were planted before the problem than after the problem.

The new ratio of maple trees to the oak trees is 3 : 11.

And, the new trees of Oak were = 132.

Let the new maple trees be
`x.`

So, 3 is equivalent 11.

Thus,
`x` is equivalent to 132.

Now, to solve using cross multiplication method:

`(3)/(11) =(x)/(132)`

By cross multiplying we get:

`396=11x`

Dividing both sides by 11 we get:

`36=x\\\\x=36.`

The new maple trees were = 36.

Now, total number of trees, maple and oak both = 132+36 = 168.

According to question:

The quantity of trees planted after the bug problem and the quantity of trees planted before the bug problem were same.

So, total number of trees before the bug problem was = 168.

Now, before the bug problem the ratio of maple trees to oak trees were 9 : 5.

Let the number of maple trees before bug problem be
`9y.`

And, let the number of oak trees before bug problem be
`5y.`

Now, to get the number of maple trees before bug problem we solve an equation:

`9y+5y=168`

`14y=168`

Dividing both sides by 14 we get:

`y=12.`

Now, substituting the value of
`y`:

`9y=9* 12=72\ trees.`

There were 72 maple trees after the bug problem.

Now, to get the more trees before the bug problem than after the bug problem we subtract 36 trees that were before the bug problem from the 72 trees after the bug problem:

`72-36\\\\=36\ trees.`

Therefore, there were 36 more maple trees planted before the bug problem than after the bug problem.