Question

Shelly compared the number of oak trees to the number of maple trees as a part of a study about hardwood trees in a woodlot. She counted 9 maple trees to every 5 oak trees. Later in year there was a bug problem and many trees died. New trees were planted to make sure there was 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

With the new ratio

3 maple trees for every 11 oak trees

132 oak trees (11*12=132)
3*12 = 36 maple trees

36 maple trees plus 132 oak trees = 168 total trees

since your original ratio was 9:5 that means  9/14 of the trees were maple; so set up a proportion to find the number of trees that were maple before the bugs
$\frac{9}{14}= \frac{x}{168}$ cross multiply
14x = 1512
x= 108 maple trees before there were bugs

Finally do 108 - 36 (maple trees before, minus, maple trees after)

difference = 78 maple trees