Daniel is thinking of three consecutive odd numbers. The average of the first and second number is 40, while the average of the second and third numbers is 42. List the three numbers.

Solution

Original post to this question can be found here.

Average of 1st and 2nd numbers ----- 40

Total of 1st and 2nd numbers ----- 40 x 2 = 80

1st ----1 unit

2nd ---- 1 unit + 2

Total of 1st and 2nd ---- 2 units + 2 ---- 80

2nd ---- 1 unit + 2

3rd ---- 1 unit + 2 + 2

Total of 2nd and 3rd ---- 2 units + 6

Total of 1st and 3rd is

(2 units + 2) + (2 units + 6)

= 4 units + 8

Average of 1st and 3rd is

(4 units + 8) divided by 2

= 2 units + 4

From Total of 1st and 2nd,

2 units + 2 ----- 80

2 units ----- 80 – 2 = 78

1 unit ----- 78 divided by 2 = 39

Answer:

1st number is 39

2nd is 41

3rd is 43

This blog is managed by Song Hock Chye, author of Improve Your Thinking Skills in Maths (P1-P3 series), which is published and distributed by EPH.

## Thursday, July 23, 2009

### Rosyth Sch 2006 PSLE Math Prelim Q35 - alternative method

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## 11 comments:

Dear Mr Song

From your first step, you can already get the answer

Total of 1st and 2nd ---- 2 units + 2 ---- 80

1 unit --- 39 , which is the first number.

Why do you need to go further?

Hi Mr Song

Is Coco's approach acceptable in PSLE?

Average of 1st No. and 2nd No. = 40 ==> 1st No. = 40 - 1 = 39. 2nd No. = 40 + 1 = 41. Average of 2nd No. and 3rd No. = 42 ==> 2nd No. = 42 -1 = 41. 3rd No. = 42 + 1 = 43. Hence the 3 numbers are 39, 41 and 43.

So in Exam, all you need to write down will be 40 - 1 = 39. 40 + 1 = 41. 42 + 1 = 43. The 3 numbers are 39, 41 and 43.

To convince you that I live up to my nick "Maths Professor", you can draw a model - a big unit and a small unit. In between the 2 units mark out the average. Mark out the difference of 2. So small unit is Average - 1 and Big unit is Average + 1. Convinced?

Consecutive No. 1, 3, 5, etc. So there is a difference of 2 between consecutive no. Hence just minus 1 from ave gives the smaller no. and add 1 to ave gives the larger no.

Hi Mr Song

Is solar eclipse covered in PSLE Science syllabus?

Yes, first step can get answer.

I was explaining in detail, using the average method, as requested in the original post under the comments section.

Did not think that of unit method when I posted then.

Solar eclipse is not in many science textbooks but I have seen some schools put it in their assessment papers. Cannot remember the school and year.

Hi Mr Song

Thank you.

Questions on averages usually look easy and at first glance.But they can be difficult to grasp and tricky.

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Confused =X: can anyone help me with this?Car A left Town X for Town Y while Car B left Town Y for Town X and both cars left at the same time. The ratio of their respective speed is 5 : 4 initially. After they passed each other, Car A reduced its speed by 1/5 while Car B increased its speed by 20 %. When Car A reach Town Y, Car B was still 25 km away from Town X. What is the distance between Town X and Town Y?

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i think this method would make y'all understand better it's algebra

let x be the smallest number.

40x2=80(total of 1st and 2nd)

42x2=84(total of 2nd and 3rd)

80+84=164(sum of 1st, 3rd and 2 of the second number)

x+x+2+x+2+x+4= 164

So, 4x+8=164

164-8=156

156/4=39(1st number)

39+2=41(2nd number)

39+4=43(3rd number)

hope y'all get it :D

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