Problem:
The dimensions of a module box are: height = x+11 inches, length = x+1 inches and width = x+6 inches. If the volume of the module box is 750 cubic inches, what is the value of x?
Given:
H = x + 11
L = x + 1
W = x + 6
Solution:
V = LWH
750 = (x + 1)(x + 6)(x + 11)
750 = x³ + 18x² + 83x + 66
x³ + 18x² + 83x + 66 - 750 = 0
x³ + 18x² + 83x - 684 = 0
(x - 4)(x² + 22x + 171) = 0
x = 4
H = x + 11
H = 4 + 11
H = 15
L = x + 1
L = 4 + 1
L = 5
W = x + 6
W = 4 + 6
W = 10
Checking:
750 = (x + 1)(x + 6)(x + 11)
750 = (4 + 1)(4 + 6)(4 + 11)
750 = 5(10)(15)
750 = 750 ; ok
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