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Question
Two cubic blocks of marble, at $5 per cubic foot, were purchased for $2,340.  The combined length of the blocks were 12 feet.

Calculate length of each block.

Thanks.

Answer
"Two cubic blocks of marble, at $5 per cubic foot, were purchased for $2,340."
$2340 1 ft/$5 = 468 ft

The first block is x feet by x feet by x feet.
The second block is y feet by y feet by y feet.
Total volume = x + y = 468

"The combined length of the blocks was 12 feet."
x + y = 12
y = 12 - x

Factoring the sum of squares:
(x + y) = (x + y)(x - xy + y)
468 = 12(x - xy + y)
39 = x - xy + y

substitution
39 = x - x(12-x) + (x - 24x + 144)
3x - 36x + 105 = 0
x - 12x + 35 = 0

quadratic formula
x = [12 √(12 - 4135)]/(21)
 = [12 √4]/2
 = [12 2]/2
 = 5, 7

One block is 5 ft long. The other block is 7 feet long.

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I can answer questions in Algebra, Basic Math, Calculus, Differential Equations, Geometry, Number Theory, and Word Problems. I would not feel comfortable answering questions in Probability and Statistics or Topology because I have not studied these in depth.

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