How much wood...? #4

Number Theory Level 2

Reference to my previous three problems for important information : #1 , #2 , and #3

A year after my previous problem, the woodchuck returns home with his wife and two children. They decide to celebrate their successful journey back home by having a wood feast. How much wood could the woodchucks chuck if the woodchucks could chuck wood?

Details and Assumptions:

Each mature tree contains 10,000 cubic feet of wood. Each 6-month old sapling contains 5,000 cubic feet of wood. Assume that the trees have grown and produced offspring prior to the arrival of the woodchucks. Tree growth rates are described in my previous problem .
Our woodchuck and his wife now chuck 1 out of every 3 mature trees present at the beginning of the feast on their own (independent of each other).
The two baby woodchucks chuck 1 out of every 6 sapling trees present at the beginning of the feast (independent of each other).

Let the number of mature trees consumed be denoted as $t$ . Let the number of saplings consumed be denoted as $s$ .

What is $t$ * $s$ ?

The answer is 125000.

1 solution

Amogha Pokkulandra
Sep 16, 2017

Before the woodchuck family arrives, the 375 mature trees and 375 saplings have each had their birthdays 6 months prior to the woodchucks' arrival. 375 trees and 375 new trees (former saplings) each produce one sapling, for a total of 750 trees and 750 6-month-old saplings when the woodchucks arrive. The woodchuck and his wife combined eat 2 out of every 3 trees, so $\frac {2}{3}$ multiplied by 750 trees makes $t$ = 500 . The two babies eat together 1 out of every 3 trees, and $\frac {1}{3}$ times 750 saplings equals $s$ = 250 . $t$ * $s$ = $250 * 500$ = $\boxed {125,000}$ .

How much wood...? #4

The answer is 125000.

1 solution

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