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Find the number of ways that 75 can be expressed as the sum of two or more consecutive positive integers.

Jun 6, 2020

#1
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1  - 37  to 38 = 75
2  - 24  to 26 = 75
3  - 13  to 17 = 75
4  - 10  to 15 = 75
5  - 3  to 12 = 75

Jun 6, 2020
#2
+1

Find the number of ways that 75 can be expressed as the sum of two or more consecutive positive integers.

Hello Guest!

x+x+1+x+2+x+3+x+4+x+5+x+6+x+7+x+8+x+9+x+10+x+11+x+12=75

13x=75-78

x=-3/13

x+x+1+x+2+x+3+x+4+x+5+x+6+x+7+x+8+x+9+x+10+x+11=75

12x=75-66

x=9/12

x+x+1+x+2+x+3+x+4+x+5+x+6+x+7+x+8+x+9+x+10=75

11x=75-55

x=20/11

10x=75-45

x=3                        |   3, 4, 5, 6, 7, 8, 9, 10, 11, 12

9x=75-36

x=93/11

8x=75-28

x=47/8

7x=75-21

x=54/7

6x=75-15

x=10                     |   10, 11, 12, 13, 14, 15

5x=75-10

x=13                     |   13, 14, 15, 16, 17

4x=75-6

x=69/4

3x=75-3

x=24                     |   24, 25, 26

2x=75-1

x=37                     |   37, 38

The number of ways that 75 can be expressed as the sum of two or more consecutive positive integers is 5. !

Jun 6, 2020