blazecorn12
Answered

The diameter of a small gear is 16 cm. This is 2.5 cm more than 1/4 of the diameter of a larger gear. What is the diameter of the larger gear? (Round to the nearest centimeter)

Verified Answer :

let 'x' represent the diameter of the larger gear


2.5 + (1/4)x = 16


x = 54 cm


dexteright02

Data:

\(d = 16cm\)
\(d = 2.5* \frac{1}{4} D\)

Solving:
Substitute

\(d = 2.5* \frac{1}{4} D\)
\(16 = \frac{2.5D}{4}\)
\(16*4 = 2.5D\)
\(64 = 2.5D\)
\(2.5D = 64\)
\(D = \frac{64}{2.5}\)
\(\boxed{D=25.6cm}\)

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