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# [Smart Math] Averages Problem 12

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

### Problem

The average weight of 10 sacks of wheat is decreased by 1 lb when 2 of them 26 and 30 lbs are replaced by 2 rice sacks. What was the average weight of the two rice sacks?

1. 21 lbs
2. 22 lbs
3. 23 lbs
4. 24 lbs
5. 25 lbs

### The Usual Method

Let the average weight of 2 rice sacks be ‘x’ lbs.

Hence total weight of two rice sacks = 2x lbs.

This is substituted for two wheat sacks of 26 and 30 lbs. i.e 26 + 30 =56 lbs.

Since the average weight of 10 sacks of wheat is decreased by 1 lb, reduction in total weight = 1 x 10 = 10 lbs.

$\therefore 56-2x=10$

$\therefore 56-10=2x$

$\therefore 46=2x$

$\therefore x=23$lbs.

(Ans: 3)

Estimated Time to arrive at the answer = 30 seconds.

### Using Technique

Note that the reduction of 10 lbs in the total weight of 10 sacks is attributable to the two rice sacks. Hence, each rice sack should have 5 lbs less weight than the average weight of the two wheat sacks of 26 and 30 lbs.

Average of 26 and 30 = $\frac{26+30}{2}=\frac{56}{2}=28$lbs

Hence average weight of a sac of rice =28 – 5 = 23 lbs.

(Ans: 3)

Estimated Time to arrive at the answer = 10 seconds.
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