Answer:
1.35 meters
Step-by-step explanation:
Let the original length of the string be x.
So, we started out with x centimeters. Rachel used 2/3 of it (the original amount) to tie some books together. Therefore, we now have:
[tex]x-\frac{2}{3}x[/tex]
centimeters of string left. This represents the original minus the amount she used.
Next, she used 1/3 of the remaining string. In other words:
[tex]x-\frac{2}{3}x-\frac{1}{3}(x-\frac{2}{3} x)[/tex]
The newly added terms is 1/3 of the remaining string length.
And she ends up with 30 centimeters. Therefore, we need to solve the equation for x:
[tex]x-\frac{2}{3}x-\frac{1}{3}(x-\frac{2}{3} x) =30\\\frac{1}{3}x-\frac{1}{3}x+\frac{2}{9}x=30\\\frac{2}{9}x=30\\ x=30\cdot \frac{9}{2}=135 \text{ centimeters}[/tex]
Therefore, the original length of the string was 135 centimeters or 1.35 meters (move the decimal two places to the left).
