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, April 02, 2009

### Rosyth Sch 2006 PSLE Math Prelim Q35

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

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

Average of 2nd and 3rd ----- 42
Total of 2nd and 3rd ----- 42 x 2 = 84

Total of 1st and 3rd -----
(80 + 84) divided by 2 = 82

Average of 1st and 3rd -----
82 divided by 2 = 41

41 is also the middle number.
1st and 3rd numbers ----- 39 and 43

Anonymous said...

i don't understand

confused said...

why is the total of the 1st and 3rd number equal to 80+84 divided by 2 ?

Excel Eduservice said...

The total of the 1st and 3rd is the average of the (total of 1st and 2nd) and (total of 2nd and 3rd).

Anonymous said...

Dear Mr Song

The total of the 1st and 3rd is the average of the (total of 1st and 2nd) and (total of 2nd and 3rd).

Could you help to elaborate on this?Any simpler method to solve this problem?

Anonymous said...

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.

Another way is using algebra.

Let the first smallest odd number be x.

If x = 1,

then the next two odd number will be as such:

x + 2, x + 4.

Thus from ascending order,

x , x + 2 , x + 4

x + x + 2 = 40 x 2 = 80
2x = 78
x = 39

since smaller odd number is 39,
the following 2 numbers are

39 + 2 = 41 and 39 + 4 = 43

Alternatively,

x + 2 + x + 4 = 42 x 2 = 84

2x = 78
x = 39
...
...
...

Excel Eduservice said...

Anonymous said...

here is a easier method:1st+2nd=80
2nd+3rd=84
(3rd+2nd)-(1st+2nd)=4
diff of 1st and 3rd is 4
diff of 1st and 2nd is 2
80-2=78
78 divided 2 =39
1st=39
2nd=(39+2)=41
3rd=(41+2)=43

Anonymous said...

I also thought of that method.