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?

Question

2245 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-20T10:10:57

15 years ago

let $x$ $x$ = the growth per year in feet

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

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

but we are also told that $h_{3} = h_{2} + \frac{1}{5} \cdot h_{2}$ $h_3 = h_2 +1/5*h_2$

$h_{3} = (3 + 2 x) + (0.2 \cdot (3 + 2 x))$ $h_3 = (3 + 2x) + (0.2*(3 + 2x))$

$h_{3} = 1.2 \cdot (3 + 2 x)$ $h_3 = 1.2*(3 + 2x)$

$h_{3} = 2.4 x + 3.6$ $h_3 = 2.4x + 3.6$ ....(3)

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

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

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

$0.6 x = 0.6$ $0.6x = 0.6$

$x = \frac{0.6}{0.6} = 1$ $x = 0.6/0.6 = 1$ ft/year

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

At 1 ft/year this has taken 15 years