SOLUTION: The number 45 us truly awesome. Add 1+2+....+9=45. e.add consecutive numbers to get 45 Find 4ways to make a sum of 45 with consecutive number 12numbers......+....=45 2.3numbers.

Question 1081900: The number 45 us truly awesome. Add 1+2+....+9=45. e.add consecutive numbers to get 45
Find 4ways to make a sum of 45 with consecutive number
12numbers......+....=45
2.3numbers......+....+....=45
3.4numbers....+....+....+....=45
4.5numbers......+....+....+....+...=45
Answer 4questions please
Found 2 solutions by Fombitz, jim_thompson5910:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Duplicate question
See Answer 695920

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Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Part 1)

x = first number
x+1 = second number

Add up the two expressions and set equal to 45. Solve for x.

x+(x+1) = 45
2x+1 = 45
2x+1-1 = 45-1
2x = 44
2x/2 = 44/2
x = 22

If x = 22, then x+1 = 22+1 = 23

Note how 22+23 = 45

---------------------------------------------------------------

Part 2)

x = first number
x+1 = second number
x+2 = third number

x+(x+1)+(x+2) = 45
3x+3 = 45
3x+3-3 = 45-3
3x = 42
3x/3 = 42/3
x = 14

x = 14
x+1 = 14+1 = 15
x+2 = 14+2 = 16

So,
14+15+16 = 45

---------------------------------------------------------------

Part 3)

x = first number
x+1 = second number
x+2 = third number
x+3 = fourth number

x+(x+1)+(x+2)+(x+3) = 45
4x+6 = 45
4x+6-6 = 45-6
4x = 39
4x/4 = 39/4
x = 9.75

9.75 isn't a whole number so it's impossible to add up four consecutive integers to get 45.

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Part 4)

x = first number
x+1 = second number
x+2 = third number
x+3 = fourth number
x+4 = fifth number

x+(x+1)+(x+2)+(x+3)+(x+4) = 45
5x+10 = 45
5x+10-10 = 45-10
5x = 35
5x/5 = 35/5
x = 7

x = 7
x+1 = 7+1 = 8
x+2 = 7+2 = 9
x+3 = 7+3 = 10
x+4 = 7+4 = 11

So,
7+8+9+10+11 = 45

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In summary,
Adding 2 consecutive integers: 22+23 = 45
Adding 3 consecutive integers: 14+15+16 = 45
Adding 4 consecutive integers: not possible
Adding 5 consecutive integers: 7+8+9+10+11 = 45

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