Question

The heights of a maple tree and a cherry tree have a ratio of 5:2. If the maple tree grew 20 cm and 20 cm was cut off the top of the cherry tree, the ratio of their heights would be 3:1. How much taller is the maple tree than the cherry tree?

Answer 1

Let x be the heights of a maple tree and y be the height of the cherry tree.
We know:

`(x)/(y) = (5)/(2)`
The new ratio is obtained like this:

`(x+20)/(y-20) = (3)/(1)`.
From the above equation we get
`x= (y-20)(3)/(1) -20`.
then
`( (y-20)(3)/(1) -20)/(y) = (5)/(2)`
Solving the above equation for y we get:
`y=160`
So
`x=400`
So the first tree is (400-160=240) more taller than cherry tree.