<PRE><B>Question 628205</B>
A rectangular garden is 60 ft by 80 ft.
 Part of the garden is torn up to install a sidewalk of uniform width around the garden.
 The new area of the garden is one sixth of the old area.
 How wide is the sidewalk?
:
Let x = the width of the walk
:
The new dimensions of the garden will be (60-2x) by (80-2x)
:
Find the original area: 60*80 = 4800 sq/ft
Find the new area: {{{1/6}}}*4800 = 800 sq/ft
:
(60-2x)*(80-2x) = 800
FOIL
4800 - 120x - 160x + 4x^2 = 800
Combine on the left as a quadratic equation
4x^2 - 280x + 4800 - 800 = 0
4x^2 - 280x + 4000 = 0
simplify divide by 4
x^2 - 70x + 1000 = 0
Factors to
(x-20)(x-50) = 0
Two solutions
x = 50, not reasonable
and
x = 20 ft is the width of the walk
:
:
Check this with the new dimensions (2x = 40):
 (80-40)*(60-40) = 800 sq/ft
</PRE>