Problema Solution
A model of carry-on luggage has a length that is 66 inches greater than its depth. Airline regulations require that the sum of the length, width, and depth cannot exceed 28 inches. These conditions, with the assumption that this sum is 28 inches, can be modeled by the function V(x) that gives the luggage's volume, in cubic inches, in terms of its depth, x, in inches. If its volume is 540 cubic inches, determine two possibilities for its depth.
Answer provided by our tutors
depth = x
length = x + 66
width = 28 - (x + x + 66)
width = 2x - 38, 2x - 38 >= 0 , x >= 19
V(x) = depth * length * width
V(x) = x * (x+66) * [2x - 38]
V(x) = x(x+66)(2x - 38)
the volume is 540 cubic inches meaning:
x(x+66)(2x - 38) = 540 divide both sides by 2
x(x+66)(x - 19) = = 270
by solving we find three real solutions:
x1 = 0.22 in
x2 = 18.70 in
x3 = 66.09 in
Since x must be greater than 19 follows there is only one possibility for the depth: 66.09 in.