waecmaths question:
The mean age of R men in a club is 50 years. Two men aged 55 and 63, left the club and the mean age reduced by 1 year. Find the value of R
Option A:
18
Option B:
20
Option C:
22
Option D:
28
waecmaths solution:
\[\begin{align} & \overline{{{x}_{1}}}=\frac{R}{n}=50 \\ & R=50n----(i) \\ & \text{When the two men left, whose sum is 113} \\ & \overline{{{x}_{2}}}=49 \\ & \overline{x}=\frac{R-113}{n-2}=49 \\ & R-113=49(n-2) \\ & R-113=49n-98 \\ & R-49n=113-98 \\ & R-49n=15 \\ & \text{substitute }R=50n\text{ from }(i) \\ & 50n-49n=15 \\ & n=15 \\ & R=50n=50\times 15=750 \\\end{align}\]
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