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(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(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}\\ (7)/(4)&365\\\\ (63)/(4)&d \end{array}\implies \cfrac{(7)/(4)}{(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}`