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

**Problem**

**Problem**

The average temperature for the first 9 days was 20 C and that of the first 5 was 25 C and that for the last 5 days was 15 C. What was the temperature on the fifth day?

- 25 C
- 20 C
- 30 C
- 15 C
- 27 C

**The Usual Method**

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Total temperature for 9 days = 9 x 20 = 180 C

Total temperature for first 5 days = 5 x 25 = 125 C

Total temperature for last 5 days = 5 x 15 = 75 C

Also, total temperature for first 5 days = *a* + *b*

Where, *a* = total temperature for first 4 days and

*b* = temperature on the 5^{th} day

Similarly, total temperature for last 5 days = *b* + *c*

Where, *b* = temperature on the 5^{th} day and

*c* = total temperature for last 4 days

…… Eq. 1.

and …… Eq. 2.

Also

Adding Eq. 1 and Eq. 2, we get: *a* + 2*b* + *c* = 200 C

20 C

Hence, temperature on 5^{th} day = 20 C

**(Ans: 2)**

*Estimated Time to arrive at the answer = 45 seconds.*

**Using Technique**

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Since the average temperatures for the first 5 days and the last 5 days is ‘equidistant’ from the average temperature for the 9 days, we can simply take the arithmetic mean of 25 and 15 as 20 C as the temperature of the 5^{th} day.

**(Ans: 2)**

*Estimated Time to arrive at the answer = 5 seconds.*

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