M and N share a rented property. M uses 16 machines for 6 months, while N uses 24 equipment for 5 months and 36 tools for 4 months. If 3 machines are equivalent to 6 equipment, and 2 equipment equal 3 tools. What portion of rent does M pay?

Question

Accepted Answer

1. Convert units: from $3$ machines = $6$ equipment gives $1$ machine = $2$ equipment. From $2$ equipment = $3$ tools gives $1$ tool = $2/3$ equipment.

2. M's use in equipment-months: $16$ machines = $16	imes2=32$ equipment. Over $6$ months: $32	imes6=192$.

3. N's use: $24$ equipment for $5$ months = $24	imes5=120$. 36 tools = $36	imes	frac{2}{3}=24$ equipment. For $4$ months: $24	imes4=96$. So N total = $120+96=216$.

4. Total = $192+216=408$. M's share = $\dfrac{192}{408}=\dfrac{8}{17}$.

FINAL_ANSWER: d

Answer

Answer

Answer