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 big problem and many trees died. New trees were planted to make sure there was the same number of trees as before the big 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 big problem than after the bug problem? Explain.

Answer 1

Try this option:
1. according to the condition new ratio of maple trees (m.t.) is 3:11 and number of o.t. is 132. It means

`(3)/(11) = (x_1)/(132) \ =\ \textgreater \ \ x_1=3*132/11=36(m.t.)` number of m.t. after the bug.
2. total number of trees after bug problem is 132+36=168. According the condition it is the same number as before the big problem. Using this,
3. 5x+9x=168 - total number of the trees before big problem, where 5x is number of o.t. and 9x is number of m.t.
x=168/14=12 and
4. ⇒ 9x=9*12=108 m.t. before the big problem.
answer: 36 m.t. and 108 m.t.
P.S. before the big problem 108 m.t. and 5*12=60 o.t., after the bug 36 m.t. and 132 o.t.