A Nice Story

Algebra Level pending

A poet met a tortoise under a tree. When the tortoise was the poet's current age, the poet was one-fourth of his current age. When the tree was the tortoise's current age, the tortoise was one-seventh of its current age. If the sum of the ages of the poet, tree and tortoise is 264 years, find the age of the tree in years.

Note: Their age is the total number of years completed in their lifetime. The number of months and days can be omitted. For example, if one's age is 23 years, 4 months and 3 days, then consider their age as 23.

The answer is 143.

1 solution

Chew-Seong Cheong
Mar 8, 2020

Let the ages of the poet, tortoise, and tree be $x$ , $y$ , and $z$ respectively.

When the poet was one-fourth his current age that is $\frac 14 x$ , which was $x - \frac 14 x$ years ago, the tortoise, current age $y - \left(x - \frac x4\right)$ was $x$ years old. In algebraic equation, we have:

$\begin{aligned} y - \left(x - \frac x4 \right) & = x \\ \implies y & = x + x - \frac x4 = \frac 74x \end{aligned}$

Similarly,

$\begin{aligned} z - \left(y - \frac y7 \right) & = y \\ \implies z & = y + y - \frac y7 = \frac {13}7y = \frac {13}7 \times \frac 74 x = \frac {13}4x \end{aligned}$

Then we have:

$\begin{aligned} x+y+z & = 264 \\ x + \frac 74 x + \frac {13}4x & = 264 \\ 6 x & = 264 \\ \implies x & = 44 \\ z & = \frac {13}4 \times 44 = \boxed{143} \end{aligned}$

Sir, your solutions are beautifully illustrated.

Aryan Sanghi - 1 year, 3 months ago

Glad that you like it.

Chew-Seong Cheong - 1 year, 3 months ago

A Nice Story

The answer is 143.

1 solution

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