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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

quadratic formula

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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