SOLUTION: Please help me solve this word problem: The Jones Family have a rectangular swimming pool.The pool is 5 metres longer than it is wide. There is a two metre wide strip i f paving

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Please help me solve this word problem: The Jones Family have a rectangular swimming pool.The pool is 5 metres longer than it is wide. There is a two metre wide strip i f paving       Log On


   

Question 985630: Please help me solve this word problem:
The Jones Family have a rectangular swimming pool.The pool is 5 metres longer than it is wide. There is a two metre wide strip i f paving around the pool as shown in the diagram. The area of the paving is 54 square metres. Use thus info to find the width of the swimming pool.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
w, pool width
L, pool length
k, how much longer than wide
u, uniform border width around pool
A, area of the border
-
w=unknown
L=w%2Bk=unknown
k=5
u=2
A=54

wL=poolArea
%28w%2B2u%29%28L%2B2u%29=totalArea
highlight_green%28%28w%2B2u%29%28L%2B2u%29-wL=A%29, to relate areas to given border area

First solve for w.
wL%2B2uL%2B2uw%2B4u%5E2-wL=A
2uL%2B2uw%2B4u%5E2=A
2u%28w%2Bk%29%2B2uw=A-4u%5E2
4uw%2B2uk=A-4u%5E2
4uw=A-4u%5E2-2uk
highlight_green%28w=%28A-4u%5E2-2uk%29%2F%284u%29%29

Substitute the known values and evaluate w.
w=%2854-4%2A2%5E2-2%2A2%2A5%29%2F%284%2A2%29
highlight%28highlight%28w=9%2F4%29%29

Use w now found, to evaluate L.
L=9%2F4%2B5
highlight%28highlight%28L=29%2F4%29%29