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?
Let x be the heights of a maple tree and y be the height of the cherry tree. We know: [tex] \frac{x}{y} = \frac{5}{2} [/tex] The new ratio is obtained like this: [tex] \frac{x+20}{y-20} = \frac{3}{1} [/tex]. From the above equation we get [tex] x= (y-20)\frac{3}{1} -20[/tex]. then [tex] \frac{ (y-20)\frac{3}{1} -20}{y} = \frac{5}{2} [/tex] Solving the above equation for y we get: [tex]y=160[/tex] So [tex]x=400[/tex] So the first tree is (400-160=240) more taller than cherry tree.
