Here’s and example of a SMART MATH problem for AVERAGES.
Problem
The average weight of a sac of wheat in a truck is reduced by 0.2 lbs from 50 lbs when 5 new sacs, each weighing 47.4 lbs on an average, are loaded. How many sacs did the truck originally carried?
- 60
- 62
- 64
- 66
- 68
The Usual Method
[contentblock id=google-adsense-post]
Let there be ‘x’ number of sacs in the truck originally.
Hence total weight of the load in the truck = 50x
New number of sacs = x + 5
New average weight = = (49.8x + 249) lbs
Total weight of new sacs = 47.4 x 5 = 237 lbs
Hence 49.8x + 249 = 50x + 237
(Ans: 1)
Estimated Time to arrive at the answer = 60 seconds.
Using Technique
[contentblock id=google-adsense-post]
Difference between the average weight of the original sacs and the new sacs = 50 – 47.4 = 2.6lbs
Total difference = 2.6 x 5 = 13 lbs. Now this 13 lbs is reduced from the total weight of (x + 5) bags and the reduction is that of 0.2 lb each. Hence
lbs
(Ans: 1)
Estimated Time to arrive at the answer = 15 seconds.
[starrater tpl=10]
[contentblock id=smartmath-blockquote]