Shelly 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 was the same number of trees as before the bug problem. The new ratio of the number of map;e trees to the number of oal 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?
Later tree count m:o = 3:11
So, if there were 3x maples and 11x oaks, x=12. There were
36 maples and 132 oaks.
that makes 168 trees in all
Original tree count: m:o = 9:5
So, there were 9x maples and 5x oaks, and
9x+5x = 168
x = 12
There were 108 maples and 60 oaks.
The maples fell from 108 to 36, for a difference of 72
Dun't du drugs.
have a nice day
Steve has the correct solution, but the method used in the Common Core lesson involves proportions.
The current ratio of maple to oak trees is 3:11 and there are now 132 oak trees.
3 maple trees X maple trees
------------- = ---------------
11 oak trees 132 oak trees
using cross multiplication,
11x = 396 divide both sides by 11 to get
x = 36
So now there are 36 maple trees.
Because there were new trees planted after the bugs to make the same number f trees before and after the bugs, we know there are 36 + 132 = 168 total trees. We use this total in the other proportion to solve.
Before the bugs, we know the ratio was 9 maple trees to 5 oak trees. However, this next proportion needs to find the number of maple trees using the total number of trees. So we add the trees in this ratio for a total number of trees to use in this ratio. 9 + 5 = 14. So the ratio of maple tree to the total number of trees is 9:14. This is used in the second proportion.
9 maple trees X maple trees
------------- = ---------------
14 total trees 168 total trees
Using cross multiplication, we get
14x = (9)(168)
14x = 1512 dividing both sides by 14,
x = 108
So there were 108 maple trees before bugs.
From the earlier proportion, there are now 36 maple trees.
So there were 108 - 36 = 72 more maple trees before the bugs.
This is not what I would consider a 6th grade math problem, especially considering I found 2 adults who got confused by this process, so I have no problems with posting the complete solution here.