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Averages Smart Math

[Smart Math] Averages Problem 15

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

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

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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

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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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