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UKMT Intermediate Mathematical Challenge, 2017

Algebra Difficulty 2.0 Junior Find the answer United Kingdom

Brachycephalus frogs are tiny − less than $1$ cm long − and have three toes on each foot and two fingers on each 'hand', whereas the common frog has five toes on each foot and four fingers on each 'hand'. Some Brachycephalus and common frogs are in a bucket. Each frog has all its fingers and toes. Between them they have $122$ toes and $92$ fingers. How many frogs are in the bucket?

(A) $15$ (B) $17$ (C) $19$ (D) $21$ (E) $23$

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