# Primary School "Average" Question

#### maninthemirror

##### New member
Pamela found the average of some numbers to be 124.5. She realized that she had keyed in one number wrongly. Instead of keying in 153, she keyed in 135. The actual average was 129. How many numbers were there?

#### Harry_the_cat

##### Senior Member
How much bigger was the number she keyed in compared to the number she should have keyed in? What effect did this have on the average?

#### Dr.Peterson

##### Elite Member
Pamela found the average of some numbers to be 124.5. She realized that she had keyed in one number wrongly. Instead of keying in 153, she keyed in 135. The actual average was 129. How many numbers were there?

This can be solved more easily (in the sense of needing less special thinking) by a little algebra. Have you (or the student) learned any?

On the other hand, Harry's approach uses number sense well. Since the sum of the numbers is divided by n, anything you add to that sum (in making a correction, for example) is also divided by n.

#### JeffM

##### Elite Member
If you know some algebra, this is a relatively easy problem. As a pure arithmetic problem, it is a nightmare.

$$\displaystyle c = \text {correct total.}$$

$$\displaystyle i = \text {incorrect total.}$$

$$\displaystyle n = \text {number of items.}$$

$$\displaystyle c - i = 153 - 135.$$.......................................edited

$$\displaystyle \dfrac{c}{n} - \dfrac{i}{n} = 129 - 124.5.$$

Can you solve it now?

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#### maninthemirror

##### New member
What
If you know some algebra, this is a relatively easy problem. As a pure arithmetic problem, it is a nightmare.

$$\displaystyle c = \text {correct total.}$$

$$\displaystyle i = \text {incorrect total.}$$

$$\displaystyle n = \text {number of items.}$$

$$\displaystyle c - f = 153 - 135.$$

$$\displaystyle \dfrac{c}{n} - \dfrac{i}{n} = 129 - 124.5.$$

Can you solve it now?
What is f?

#### JeffM

##### Elite Member
Oops. That f should be i. Sorry.

#### Harry_the_cat

##### Senior Member
Yes I was assuming no algebra was involved.