SOLUTION: A 45 foot rope is to be cut into 3 pieces. The second piece must be twice as long as the first piece and the third piece must be 9 feet longer than 3 times the length of the second

Question 211424: A 45 foot rope is to be cut into 3 pieces. The second piece must be twice as long as the first piece and the third piece must be 9 feet longer than 3 times the length of the second piece. How long should each of the three pieces be?
I know:
x= the 1st piece
2x= the second piece
Found 2 solutions by nerdybill, rapaljer:
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
A 45 foot rope is to be cut into 3 pieces. The second piece must be twice as long as the first piece and the third piece must be 9 feet longer than 3 times the length of the second piece. How long should each of the three pieces be?
.
Good start:
x= the 1st piece
2x= the second piece
From: "the third piece must be 9 feet longer than 3 times the length of the second piece" we have:
3(2x)+9 = the third piece
.
x + 2x + 3(2x)+9 = 45
x + 2x + 6x + 9 = 45
9x + 9 = 45
9x = 36
x = 4 feet (1st piece)
.
2x= 2*4= 8 feet (2nd piece)
.
3(2x)+9 = 3(8)+9 = 24+9 = 33 feet (3rd piece)
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
You are correct!

Let x = first piece
2x = second piece
3(2x) + 9 = third piece

Add them up for the equation:
x + 2x + 6x + 9 = 45
9x + 9 = 45
9x = 36
x = 4 First piece
2x = 8 Second piece
6x+ 9
6*4 + 9 =24+9=33 Third piece

Check: See if it adds up to 45 feet
4 + 8+ 33 = 12+ 33 = 45
It checks!!

For additonal explanation, examples, and exercises like these Word Problems, please see my own website by clicking on my tutor name "Rapaljer" anywhere in algebra.com. Look for "Basic, Intermediate, and College Algebra: One Step at a Time". Choose "Basic Algebra" and look in Chapter 1 for "Word Problems". Many of these exercises are then solved on the "MATH IN LIVING COLOR" pages that are associated with this section. You really need my "non-traditional" explanation to appreciate the fact that Word Problems aren't as hard as you thought they were!!

R^2

Dr. Robert J. Rapalje, Retired
Seminole Community College
Altamonte Springs, FL 32714

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