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Question Number 92 by michelle last updated on 25/Jan/15
Six friends have an average height of 167 cm Mike with height 162 cm leaves. What is the new average?
$$\mathrm{Six}\:\mathrm{friends}\:\mathrm{have}\:\mathrm{an}\:\mathrm{average}\:\mathrm{height}\:\mathrm{of}\:\mathrm{167}\:\mathrm{cm} \\ $$$$\mathrm{Mike}\:\mathrm{with}\:\mathrm{height}\:\mathrm{162}\:\mathrm{cm}\:\mathrm{leaves}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{new}\:\mathrm{average}? \\ $$
Commented by Rasheed Soomro last updated on 09/Jun/16
Total of six friends′ heights=167×6 Total of five friends′ heights=167×6−162 [without Mikd] New average=((167×6−162)/5)=168
$$\mathcal{T}{otal}\:{of}\:{six}\:{friends}'\:{heights}=\mathrm{167}×\mathrm{6} \\ $$$$\mathcal{T}{otal}\:{of}\:{five}\:{friends}'\:{heights}=\mathrm{167}×\mathrm{6}−\mathrm{162}\:\left[{without}\:{Mikd}\right] \\ $$$${New}\:{average}=\frac{\mathrm{167}×\mathrm{6}−\mathrm{162}}{\mathrm{5}}=\mathrm{168} \\ $$
Answered by rajabhay last updated on 03/Dec/14
Let x be the new average 5x+162=167×6 5x+162=1002 5x=1002−162=840 x=168
$$\mathrm{Let}\:{x}\:\mathrm{be}\:\mathrm{the}\:\mathrm{new}\:\mathrm{average} \\ $$$$\mathrm{5}{x}+\mathrm{162}=\mathrm{167}×\mathrm{6} \\ $$$$\mathrm{5}{x}+\mathrm{162}=\mathrm{1002} \\ $$$$\mathrm{5}{x}=\mathrm{1002}−\mathrm{162}=\mathrm{840} \\ $$$${x}=\mathrm{168} \\ $$

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