Two men, M and N, rent a pasture. M uses 12 cows for 4 months and 18 goats for 5 months, while N uses 26 goats for 7 months. If 3 cows are equivalent to 7 goats, what is M's share of the rent?

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1. Convert cows to goats: $3	ext{ cows}=7	ext{ goats}$ so $1	ext{ cow}=	frac{7}{3}	ext{ goats}$. Thus $12$ cows $=12	imes	frac{7}{3}=28$ goats.

2. M's goat-months: cows give $28	imes4=112$ and goats give $18	imes5=90$. Total $=112+90=202$.

3. N's goat-months: $26	imes7=182$.

4. M's share $=\dfrac{202}{202+182}=\dfrac{202}{384}=\dfrac{101}{192}$. This is option (a).

FINAL_ANSWER: a

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