The Belt Doubt!

Algebra Level 2

A magic wish-granting rectangular belt always shrinks to $\frac 1 2$ its length and $\frac 1 3$ its width whenever its owner makes a wish. After three wishes, the surface area of the belt's front side was $4 \text{ cm}^2$ .

If the original width was $9 \text{ cm}$ , what was the original length in $\text{cm}$ ?

The answer is 96.

1 solution

Feathery Studio
Mar 19, 2015

Make one wish: $(\frac{l}{2})(\frac{w}{3}) = \frac{lw}{6}$ or $(lw)\frac{1}{6}$

Since the belt becomes $\frac{1}{6}$ of its original area after a wish, three wishes means that it becomes a sixth of its original size each three times, or:

$(lw)(\frac{1}{6})(\frac{1}{6})(\frac{1}{6}) = \frac{lw}{6^{3}} = \frac{lw}{216}$

So now,

$\frac{l(9)}{216} = 4$

$9l = 864$

$l=\boxed{96}$

thanks for giving me the explanation

Amrit Nimiyar - 6 years, 1 month ago

The Belt Doubt!

The answer is 96.

1 solution

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