SOLUTION: Hi, I hope you could help me out with this problem within our book concerning word problems on simultaneous systems involving quadratic. The cost for building a rectangular vat wi

Question 952780: Hi, I hope you could help me out with this problem within our book concerning word problems on simultaneous systems involving quadratic. The cost for building a rectangular vat with a square base was $128. the base cost $0.30/sq. ft, and the sides cost $0.20 sq ft. Find the dimensions of the vat if the combined area of the base and sides was 512 sq ft.
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
B=base area; S=side area
B+S=512 sq ft
B=512 sq ft-S
$0.30B+$0.20S=$128 Substitute for B.
$0.30(512sqft-S)+$0.20S=$128
$153.6-$0.30S+$0.20S=$128 Subtract $128 from each side.
$25.60-$0.10S=0 Add $0.10S to each side
$25.60=$0.10S Divide each side by $0.10
256 sq ft=S The area of the sides is 256 sq ft.
B=512 sq ft- 256 sq ft=256 sq ft The area of the base is 256 sq ft
Area of square=S^2
256 sq ft=S^2 Find square root of each side
16 ft=S ANSWER 1 The sides of the base are 16 feet.
Perimeter of Base=2(L+W)=2(16ft+16ft)=2(32ft)=64 ft
Area of sides=(perimeter of base)(height)
256 sq ft=(64 ft)(height) Divide each side by 64 feet.
256 sq ft/64 ft=height
4 feet=height ANSWER 2: The height is 4 feet.
ANSWER: The dimensions of the vat are 16 ft long by 16 ft wide by 4 ft high.

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