Question posted by Joyce Sim from Singapore:
Grade/Level: Primary 4
Question: Average of a number of files is $4. After buying another file which cost $16, the average increases to $7. Find the number of files at the beginning.
Step 1: This question involves the Total Vs Individual Difference Concept. First, we draw 1 box to represent the old average of $4. Then we draw an arrow to the right to show that this box is repeated by an unknown number of times (label "?" at the end of the arrow).
Step 2: Then, we draw 1 box to represent the new average of $7. Then we draw an arrow to the right to show that this box is repeated by an unknown number of times (label "?" at the end of the arrow).
Step 3: Usually, for this type of questions, we are comparing an equal number of groups. Since the difference between the first and the second scenario is 1 extra file which increases the average to $7, we will subtract $7 from the $16 so that the number of files in both scenarios are the same to facilitate comparison. Thus, we can conclude that the number of files between the 2 scenarios should be the same. The only difference is that the total for the second scenario is greater than the first by $9. This value is known as the Total Difference.
We also can see from the model that the difference in average between 1 file in the old scenario and the new scenario is $7 - $4 = $3. This is known as the Individual Difference.
Total Difference / Individual Difference = Number of Groups
$9 / $3 = 3 groups
Therefore, there were 3 files at the beginning.
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