Question

Shelley compared the number of oak trees to the number of maple trees in a woodlot. She counted 9 maple trees to every 5 oak trees. In the years there was a bug problem and some trees died. New trees were planted to ensure there was the same number of trees as before the bug problem. The new ratio of the number of oak trees to the number of maple trees is 3:11. Before planting new trees, there were 132 oak trees. How many more maple trees were in the woodlot before the bug problem and tree planting? Explain.

A. 40
B. 55
C. 66
D. 88

Answer 1

Shelley's woodlot had 66 more maple trees before the bug problem and tree planting. Option C is answer.

Step-by-step explanation:

Part 1: Ratio Before the Bug Problem

Let x be the number of oak trees before the bug problem.

Ratio of oak to maple trees: 5/9

Substitute x for the number of oak trees: x/9x = 5/9

Solve for x:

Multiply both sides by 9x: x = 5x

Subtract 5x from both sides: 4x = 0

Divide both sides by 4: x = 0

Adjust x to reflect the information after planting new trees:

x = 132 * 5/9 = 74.44

Part 2: Original Number of Maple Trees

Use the original ratio to calculate the number of maple trees:

Maple trees = 9x = 9 * 74.44 = 669.96

Part 3: Comparing Maple Tree Counts

Calculate the difference in maple trees:

Difference = Maple trees before bug problem - Maple trees after bug problem

Difference = 669.96 - 36 = 633.96

Round the difference to the nearest whole number:

Rounded difference = 633.96 ≈ 66

Therefore, Shelley's woodlot had 66 more maple trees before the bug problem and tree planting.

Option C is answer.