Meredith has three bamboo poles of different lengths. The total combined length of the three poles when placed end to end is 47.5 cm. Pole B is 1.75 times as long as pole A, and pole C is 2.5 cm longer than Pole A. How long is pole C?
Let 'x' be the length of pole A.
Therefore, the length of pole B is 1.75*x.
And the length of pole C is x + 2.5.
The total length of the three poles is x + 1.75*x + x + 2.5 = 47.5 cm.
Combining like terms, we get 3.75*x + 2.5 = 47.5 cm.
Subtracting 2.5 from both sides, we get 3.75*x = 45.
Dividing both sides by 3.75, we get x = 12.
Thus, the length of pole C is 12 + 2.5 = <<12+2.5=14.5>>14.5 cm. Answer: \boxed{14.5}.