I planted a 3 ft tree that has grown the same amount each year.at the end of the third year , the tree was 1/5 taller than it was at the end of the second year .the tree is now 18 feet tall. How many years ago did I plant the tree?

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Answer 1 · 2018-07-20T10:10:57

15 years ago

let $x$ = the growth per year in feet

at the end of year 2, height
$h_2 = 3 + 2x$ .....(1)

at the end of year 3, height
$h_3 = (3 + 3x)$ ....(2)

but we are also told that $h_3 = h_2 +1/5*h_2$

$h_3 = (3 + 2x) + (0.2*(3 + 2x))$

$h_3 = 1.2*(3 + 2x)$

$h_3 = 2.4x + 3.6$ ....(3)

combining eqns (2) and (3) (both equal to $h_3$ )

$3 + 3x = 2.4x + 3.6$

$3x - 2.4x = + 3.6 - 3$

$0.6x = 0.6$

$x = 0.6/0.6 = 1$ ft/year

Total growth since planting $= 18 - 3 =15$ ft

At 1 ft/year this has taken 15 years