Question

Rachel used 2/3 of a string to tie some books together. She used 1/3 of the remaining string for his art project. She had 30cm of the string left. What was the orignal length of string. Express your ans in meter.

Answer 1

135 cm or 1.35 m

Explanation:

2/3(135) = 90

1/3(90) = 30

Answer 2

1.35 meters

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:

`x-(2)/(3)x`

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:

`x-(2)/(3)x-(1)/(3)(x-(2)/(3) x)`

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:

`x-(2)/(3)x-(1)/(3)(x-(2)/(3) x) =30\\(1)/(3)x-(1)/(3)x+(2)/(9)x=30\\(2)/(9)x=30\\ x=30\cdot (9)/(2)=135 \text{ centimeters}`

Therefore, the original length of the string was 135 centimeters or 1.35 meters (move the decimal two places to the left).