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
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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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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