SOLUTION: Please Help me to solve this word problem A vertical wall was built around a rectangular court to a certain height. The width of the adjacent side was 5 m. less than 6 times the

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Question 1165287: Please Help me to solve this word problem
A vertical wall was built around a rectangular court to a certain height. The width of the adjacent side was 5 m. less than 6 times the height of the wall and the length of one side of the court was 2 m. less than 8 times the height of the wall. The floor area of the court was greater than the area of the inside face of the wall by 178m.
a.) Determine the length of the rectangular court.
b.) Determine the width of the rectangular court.
c. Determine the number of gallons needed to paint the inside portion of the wall only. Use 4 coatings and assume one gallon has a spreading capacity of 400 sq.ft of wall.
Thank you in advance
Answer by Seutip(231) (Show Source):
You can put this solution on YOUR website!
Let
w be width
l be length
h be height
w=6h-5
l=8h-2
Floor area of court = l*w
Area of the inside face of the wall = 2l*h+2w*h
Equation: (l*w)-178=2l*h+2w*h
Find l and w,
(8h-2)(6h-5)-178=(2)(6h-5)(h)+(2)(8h-2)(h)
Solving this will give you
h=4m
w=19m
l=30m
Floor area of court = 570m^2
Area of the inside face of the wall =392m^2
1m =3.28ft

4217*4 because 4 coatings then divide by 400
4217*4/400=42.17 gallons
Hope that helps!!!