Question 271320: Find two consecutive natural numbers such that the difference of their reciprocals is one-fourth the reciprocal of the smaller number. Answer by unlockmath(1688) (Show Source):
You can put this solution on YOUR website! Hello,
Let x represent the first number and (x+1) be the next. The reciprocal of these would be 1/x and 1/(x+1). Now we can write an equation like this:
(1/x)-1/(x+1)=1/4(1/x) First off let's remove the fractions by multiplying by 4x(x+1)
which will give us:
4(x+1)-4x=x+1 Rewritten as:
4x+4-4x=x+1 Combine like terms and subtract 1 from both sides to get:
3=x or
x=3
so the natural numbers would be 3 and 4.
Good problem. RJ
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