Question

Shelley compared the number of oak trees to the number of maple trees as part of a study about hardwood trees in a woodlot. She counted 9 maple trees to every 5 oak trees. Later in the year there was a bug problem, and many trees died. New trees were planted to make sure there were the same number of trees as before the bug problem. The new ratio of the number of maple trees to the number of oak trees is 3:11. After planting new trees, there were 132 oak trees. How many more maple trees were in the woodlot before the bug problem than after the bug problem?

Answer 1

72 more trees before the bug problem

Explanation:

The ratio was 9:5 before the bug problem and 3:11 after.

After the bug problem there were 132 oak trees,

m : 132 = 3 : 11

Then we know

m/132 = 3/11

Multiplying both sides by 132 cancels on the left

132 × (m/132) = (3/11) × 132

m = (3/11) × 132

Then solving for m

m = 132 × (3/11)

m = 36 This gives us the number of trees after the bug problem.

This would give us 168 trees in total, 132 oak, and 36 maple.

Since there is the same number of trees as before we calculate the number of maple and oak previously.

If Shelley counted 9 maple for every 5 oak we know that 9 out of 14 trees are maple and 5 out of 14 trees are oak.

9/14 = .6428 which is the percentage of maple trees before the bug problem.

We multiply .6428 x 168 (the total number of trees) and we get 108.

if there are 108 maple trees then 168-108 = 60 oak trees.

Further proof:

9:5 or 9/5 = 1.8 108/60 = 1.8

108 maple trees and 60 oak before the bug problem.

So 108 (maple before bug problem) and 36 maple trees after:

108 - 36 = 72 more trees before the bug problem

Answer 2

72

Explanation:

Initial ratio of maple trees to oak trees

• 9:5

New ratio of maple trees to oak trees

• 3:11

Number of oak trees = 132

Number of maple trees

• 132*3/11 = 36

Total number of trees

• 132+36 = 168

Initial number of maple trees

• 168*9/14 = 108

The difference in the number of maple trees:

• 108 - 36 = 72