SOLUTION: If the sum of two positive integers is 43 and the difference of their squares is 43, then the smaller integer is a)17 b) 19 c) 20 d) 21

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Question 275526: If the sum of two positive integers is 43 and the difference of their squares is 43, then the smaller integer is
a)17 b) 19 c) 20 d) 21

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
If the sum of two positive integers is 43 and the difference of their squares is 43, then the smaller integer is

Let one integer be x
The other integer will be 43-x
The difference of squares = 43
x^2-(43-x)^2=43
(x+43-x)(x-43+x)=43
43(2x-43)=43
2x-43=1
2x=44
x=22
The other number will be 43-22 =21
The smaller number is 21