What is the value of $x$ which satisfies: $\frac{17}{85}+\frac{19}{95}+\frac{21}{105}+\frac{23}{115}+\frac{25}{125}+\frac{x}{135}=1$

Question

What is the value of $x$ which satisfies:

$\frac{17}{85}+\frac{19}{95}+\frac{21}{105}+\frac{23}{115}+\frac{25}{125}+\frac{x}{135}=1$

I thought $x=27$ because the numerator seems to have a pattern of adding $2$ and adding $10$ on the denominator. However, when i add it on the calculator it gives me $1.2$

Then, I just added the five terms and got $1$ so $x$ has to be $0$.

My question is Why?

Answer 1

Did you notice that the fractions are reducible?