## Model Method - Questions and Answers

Question posted by Joyce Sim from Singapore:

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.

Go To Top - Model Method - Questions and Answers

If you want us to send you our future Modelmatics eZine that would inform you on the latest article in Teach Kids Math By Model Method, do an easy sign-up below. Subscription is FREE!

 Enter your E-mail Address Here Enter your Name Here Then Don't worry — your e-mail address is totally secure. I promise to use it only to send you ModelMatics.