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# [Smart Math] Averages Problem 15

Here’s and example of a SMART MATH problem for AVERAGES. ### Problem

Nine men went to a restaurant. Eight of them spent $6 each for their meals and the ninth man spent$4 more than the average expenditure of all nine men. What is the average expenditure?

1. $5.00 2.$5.50
3. $6.50 4.$7.50
5. $10.00 ### The Usual Method [contentblock id=google-adsense-post] Total money spent by eight men = 6 x 8 =$48.00

Total money spent by 9 men = 48 + (x + 4), where ‘x’ is the average spend of all nine men.

Total money spent can also be written as = 9x

This can be equated to 48 + (x + 4). $\therefore 9x=48+(x+4)$ $\therefore 9x=x+52$ $\therefore 8x=52$ $\therefore x=\frac{52}{8}=6.50$

Hence average = $6.50 (Ans: 3) Estimated Time to arrive at the answer = 45 seconds. ### Using Technique [contentblock id=google-adsense-post] If 8 men out of 9 men spent$ 6 each, assume the average to be $6. We also know that the 9th man spent$ 4 more than the rest. This $4 has to be apportioned to the 8 men who spent$6 each. Hence, $\frac{4}{8}=0.50$ has to be added to the original spent of $6. i.e 60 + 0.50 =$6.50 which is the new average.

(Ans: 3)

Estimated Time to arrive at the answer = 15 seconds.
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