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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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