[SOLVED] Algebra word problem help

antiflux · February 5th 2007, 01:39 PM

Help I can't figure out an equation to solve this word problem..

A cement walk 1 meter wide is constructed around a circular flower bed. The Area of the flower bed is 9/16 of the entire area (flower bed and walk). What is the diameter of the flower bed?

**Singular** · February 5th 2007, 03:52 PM

let x = radius of flowerbed
The entire area = $\pi .\left( {x + 1} \right)^2$
If you know the entire area you will know x and the diameter will be 2x

**AlvinCY** · February 5th 2007, 04:26 PM

Originally Posted by antiflux

Help I can't figure out an equation to solve this word problem..

A cement walk 1 meter wide is constructed around a circular flower bed. The Area of the flower bed is 9/16 of the entire area (flower bed and walk). What is the diameter of the flower bed?

let the diameter of the flower bed be $x$ metres, the area of the flower bed is therefore $(\pi x^2) sq.m$ , therefore the area of the entire construction (flower bed and walk) = $[\pi (x + 1)^2] sq.m$

you know that $\pi x^2$ is 9/16 of $\pi (x + 1)^2$

Therefore $x^2 = \frac{9}{16}(x + 1)^2$
$16x^2 = 9x^2 + 18x + 9$
$7x^2 - 18x - 9 = 0$ , splitting the middle term;
$7x^2 - 21x + 3x - 9 = 0$
$7x(x - 3) + 3(x - 3) = 0$
$(x - 3)(7x + 3) = 0$

Therefore $x = 3$ or $x = -\frac{3}{7}$

But we said the diameter of the flower bed is $x$ , therefore $x = 3$ and $x \not = -\frac{3}{7}$ as $x$ is a length, which must be positive.

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