SOLUTION: Hi Sue wanted to cut a piece of ribbon into 2 smaller pieces. At first wanted the first piece to be 210cm . The she changed her mind and reduced it by 20cm. This would increase t

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Question 1205091: Hi
Sue wanted to cut a piece of ribbon into 2 smaller pieces. At first wanted the first piece to be 210cm . The she changed her mind and reduced it by 20cm. This would increase the length of the second piece by 8 %. What was the total length of the whole ribbon before she cut it.
Thanks

Found 2 solutions by Edwin McCravy, math_tutor2020:
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Sue wanted to cut a piece of ribbon into 2 smaller pieces.
Sue started with a piece of ribbon L cm long.
At first she wanted the first piece to be 210 cm.
At first she wanted the first piece to be 210 cm and the second piece to be
L-210.

Then she changed her mind and reduced it by 20cm.
That was the FIRST piece she changed her mind about and reduced by 20 cm. 
So she changed her mind and wanted the FIRST piece to be 210-20=190 cm instead
of 210 cm. That made the SECOND piece be L-190 instead of L-210.

This would increase the length of the second piece by 8 %.
 

%22%22=%22%22%22%22%2B%22%22%28matrix%281%2C2%2C%228%25%22%2C+of%29%29

L-190%22%22=%22%22+L-210%22%22%2B%22%22+0.08%28L-210%29

Solve that for L.

Edwin

Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

x = length of the ribbon in cm.

Initially,
1st piece = 210 cm
2nd piece = x-210 cm

Then she changes her mind
1st piece = 210-20 = 190 cm
2nd piece = x-190 cm

The new 2nd piece length (x-190) is 8% larger than the old length (x-210)

x-190 = (x-210) + 8% of (x-210)
x-190 = (x-210) + 0.08(x-210)
x-190 = 1.08(x-210)
x-190 = 1.08x-226.8
-190+226.8 = 1.08x-x
36.8 = 0.08x
x = 36.8/0.08
x = 460