Increasing 50 by x% can be written as:
[tex] 50 + \frac{x}{100} =50+0.01x [/tex].................(1)
Decreasing 70 by x % can be represented by the expression:
[tex] 70 + \frac{x}{100} =70-0.01x [/tex]...........(2)
Now we are given in the question that if we increase 50 by x% and 70 by x%, then the two values are equal.
so equating (1) and (2) , we get
[tex] 50 +0.01 x =70 - 0.01x [/tex]
bringing 0.01x to the left side:
[tex] 50 +0.01x +0.01x = 70 [/tex]
[tex] 50 +0.02x = 70 [/tex]
taking 50 to the right side, subtracting it from 70
[tex] 0.02x = 70-50 [/tex]
[tex] 0.02x = 20 [/tex]
dividing both sides by 0.02
[tex] \frac{0.02x}{0.02} =\frac{20}{0.02} [/tex]
Answer x=2000
