SOLUTION: I have a story problem!! Thank you. 223 yards of rope is to be cut into 3 parts. The second part is three more than three times the first part and the third part is 10 yards l

Question 187326: I have a story problem!! Thank you.
223 yards of rope is to be cut into 3 parts. The second part is three more than three times the first part and the third part is 10 yards less than the first. What is the length of each part.
I have this:
Let x = length of the 1st part
Let 3 + x * 3 = 2nd part
Let x - 10 = 3rd part
From there I cant figure out how to write in an equation. Gets all confusing from there.
x + 3 + ( x * 3 ) + x - 10 = 223
3x * 3 - 10 = 223
3x * ( - 7) = 223
-7
3x = 216
---------
both by 3
x = 72

Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
223 yards of rope is to be cut into 3 parts. The second part is three more than three times the first part and the third part is 10 yards less than the first. What is the length of each part.
---------------------------------------
Equations:
a + b + c = 223
b = 3a + 3
c = a - 10
----------------------------
Rearrange the equations:
a + b + c = 223
3a - b + 0 = -3
a + 0 - c = 10
---------------------------
Use any method to solve to get:
a = 46
b = 141
c = 36
================
Cheers,
Stan H.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Your analysis and equation setup were perfect. I don't quite follow how you went about solving the equation though.

In the first place you might have had less confusion if you had written it this way:

Now, collect like terms:

Add 7 to both sides:

Finally, multiply by :

So one piece is 46 yards, the second piece is 46 X 3 + 3 = 141, and the third is 46 - 10 = 36. And 46 + 141 + 36 = 223.

John

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