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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.

"Two cubic blocks of marble, at \$5 per cubic foot, were purchased for \$2,340."
\$2340 × 1 ft³/\$5 = 468 ft³

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 = x³ + y³ = 468

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

Factoring the sum of squares:
(x³ + y³) = (x + y)(x² - xy + y²)
468 = 12(x² - xy + y²)
39 = x² - xy + y²

substitution
39 = x² - x(12-x) + (x² - 24x + 144)
3x² - 36x + 105 = 0
x² - 12x + 35 = 0

x = [12 ± √(12² - 4·1·35)]/(2·1)
= [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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