**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

**Answer: 39, 41, 43**

## 8 comments:

i don't understand

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

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

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?

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

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For alternative method, Click here.

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

I also thought of that method.

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