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Question 1153553: The product of a number and the sum of the number and two is equal to 5 1/4. Find the number
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13215)   (Show Source):
Answer by ikleyn(52906)  (Show Source):
You can put this solution on YOUR website! .
Let "n" be the unknown number.
Instead of solving for "n", I will introduce x = n + 1, the number half-way between "n" and "n+2".
Then we have this equation
(x-1)*(x+1) =   , or
 = 5.25.
Then
 = 5.25 + 1 = 6.25
and
x = +/-  = +/- 2.5.
Therefore, the problem has 2 solutions for unknown number "n"
n = x-1 = 2.5 - 1 = 1.5,
or
n = x-1 = -2.5 - 1 = -3.5.
ANSWER. The problem has two solutions, n = 1.5 and/or n = -3.5.
Solved.
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Sometimes, in problems like this one, introducing a new unknown, which is exactly half-way between two unknowns values,
leads to unexpectedly fast, straightforward and elegant solution.
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