Question

A tree grows 1 3/4 feet per year. How long will it take the tree to grow from a height of 21 1/4 feet to a height of 37 feet?

Answer 1

So hmmm from 21 1/4 to 37, let's check the difference, to see how many feet is that.

$\bf 37-21\frac{1}{4}\implies 37-\cfrac{21\cdot 4+1}{4}\implies 37-\cfrac{85}{4}\impliedby LCD~is~4 \\\\\\ \cfrac{148-85}{4}\implies \cfrac{63}{4}$

so hmmm now, its growth rate is    $\bf 1\frac{3}{4}\implies \cfrac{1\cdot 4+3}{4}\implies \cfrac{7}{4}$

so.... the tree grows 7/4 in 365 days( a year ), how many days does it take it to get to 63/4 feet?

$\bf \begin{array}{ccll} \stackrel{growth}{feet}&\stackrel{time}{days}\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ \frac{7}{4}&365\\\\ \frac{63}{4}&d \end{array}\implies \cfrac{\frac{7}{4}}{\frac{63}{4}}=\cfrac{365}{d}\implies \cfrac{7}{4}\cdot \cfrac{4}{63}=\cfrac{365}{d} \\\\\\ \cfrac{28}{252}=\cfrac{365}{d}\implies d=\cfrac{252\cdot 365}{28}\implies d=\cfrac{91980}{28}\implies \boxed{d=3285}$