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 5 oak trees. Later in the year there was a bug problem and many trees died. New trees were planted to make sure there was 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? Explain.

Answer 1

Before the bug problem, there were 36 maple trees in the woodlot. After planting new trees, there were 132 oak trees. The difference in the number of maple trees before and after the bug problem is 33.

Step-by-step explanation:

To find the number of maple trees in the woodlot before the bug problem, we can use the ratio given by Shelley: 9 maple trees to 5 oak trees. Let's assume the number of maple trees before the bug problem is M and the number of oak trees is O. Using the ratio, we have the equation: 9/5 = M/O. Now, we are given that after planting new trees, there were 132 oak trees. Using the new ratio of 3:11 for maple trees to oak trees, we can set up another equation: 3/11 = M/(132). Now, we can solve these two equations simultaneously.

First, let's solve the first equation for M in terms of O: M = (9/5)O. Now, substitute this expression for M in the second equation: 3/11 = ((9/5)O)/(132). Simplifying this equation, we can multiply both sides by 132 to get rid of the fraction: 3(12) = (9/5)O. Solving for O, we have O = (3)(12)(5/9) = 20. Now, substitute this value of O back into the first equation to find M: M = (9/5)(20) = 36.

So, before the bug problem, there were 36 maple trees in the woodlot. After planting new trees, there were 132 oak trees. Now, we can calculate the difference in the number of maple trees before and after the bug problem: 36 - 3 = 33.

Answer 2

Before the bug problem, there were 36 maple trees in the woodlot. After planting new trees, there were 132 oak trees. The difference in the number of maple trees before and after the bug problem is 33.

Step-by-step explanation:

To find the number of maple trees in the woodlot before the bug problem, we can use the ratio given by Shelley: 9 maple trees to 5 oak trees. Let's assume the number of maple trees before the bug problem is M and the number of oak trees is O. Using the ratio, we have the equation: 9/5 = M/O. Now, we are given that after planting new trees, there were 132 oak trees. Using the new ratio of 3:11 for maple trees to oak trees, we can set up another equation: 3/11 = M/(132). Now, we can solve these two equations simultaneously.

First, let's solve the first equation for M in terms of O: M = (9/5)O. Now, substitute this expression for M in the second equation: 3/11 = ((9/5)O)/(132). Simplifying this equation, we can multiply both sides by 132 to get rid of the fraction: 3(12) = (9/5)O. Solving for O, we have O = (3)(12)(5/9) = 20. Now, substitute this value of O back into the first equation to find M: M = (9/5)(20) = 36.

So, before the bug problem, there were 36 maple trees in the woodlot. After planting new trees, there were 132 oak trees. Now, we can calculate the difference in the number of maple trees before and after the bug problem: 36 - 3 = 33.