Maths

y+y-y*y/y=15
y+y-y=15
y=15

2007-2006+2005-2004+.......+3-2+1=
(2007-2006)+(2005-2004)+....(3-2)+1=
1+1+1+1+1....+1=
1004

A and B are two different positive intege(r)s such that 1/A+1/B=1/3, find A*B.
1/A + 1/B = 1/3
1+ A/B = A/3
B + A = AB/3
3A + 3B = AB
AB = 3(A+B)

a+b=20 (1)
b+c=21 (2)
a+c=23 (3)
From (3), a = 23-c,
Sub this into (1),
23-c+b=20
c-b=3
Sub c=b+3 into (2)
b+b+3 = 21
2b = 18
so, b = 9

For a given book, the total number of digits for page numbers is 55. Find the number of pages in this book. (Assume the page number is 1,2,3,4,5...)
1,2,3,4,5,6,7,8,9 -> 9
10,20,30,40,50 -> 10
By logical thinking,
there are 32 pages

A and B are two different positive integes such that 1/A+1/B=1/3, find A*B.
1/A+1/B=1/3
(B+A)/AB=1/3
AB=3A+3B

a+b=20 (1)
b+c=21 (2)
a+c=23 (3)
Find B

2-1:: c-a=1...(4)
(4)+(3):: 2c=24
c=12
put c=12 into(2)
b=9

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