Question 214996
You have a pool in your backyard that is 80 foot by 60 foot. You want to build a walkway around the pool. What is the maximum width of the walkway if you only have 360 feet of fencing?
:
a.) draw a picture to model this problem.
:
Draw a rectangle (pool) inside a rectangle (fence); label the inside 80 by 60
and the the width between the pool and the fence as x
;
b.) write an expression that you could use to model this problem.
Perimeter = 2(2x+80) + 2(2x+60
Simplify
4x + 160 + 4x + 120
8x + 280 = the expression
:
c.) make a table for how much fencing you would use if the walkway was 7, 8, 9, 10, or 11 feet
:
Substitute the values for x in the above expression find the amt of fence:
 x | f in feet
-------
 7 |336
 8 |344
 9 |352
10 |360
11 |368
:
d.) write and solve an equation to find the maximum width of the walkway.
8x + 280 = 360
8x = 360 - 280
8x = 80
x = 10 ft walkway with 360' of fence
:
e.) how would this problem and solution change if you had 500 feet of fencing?
8x + 280 = 500
8x = 500 - 280
8x = 220
x = {{{220/8}}}
x = 27.5' walkway is possible