SOLUTION: write an algebraic equation which could be used to solve the following problem. then find the solution: "A 40-inch rope is cut into three pieces so that the second piece is four t

Question 385310: write an algebraic equation which could be used to solve the following problem. then find the solution: "A 40-inch rope is cut into three pieces so that the second piece is four times as long as the first and the third piece is three times as long as the first piece. Find the length of all three pieces."
im so confused
Found 3 solutions by texttutoring, mananth, vampirewitchreine:
Answer by texttutoring(324)   (Show Source): You can put this solution on YOUR website!
It appears as if you have three variables, but if you keep reading the question, you'll see you can actually express the three lengths in terms of the first.

We know the 3 lengths add up to 40.

Let's let x = the first length

We also know the second length is 4 times the first, so the second length is 4x. That means the third length must be 3x. Putting it all together:

x + 4x + 3x = 40
8x = 40
x = 40/8
x = 5

So the first length is 5 inches.

The second length is 5*4 = 20 inches
The third length is 3*5 = 15 inches.

Check that the three lengths add up to 40:

5+15+20 = 40

Yes, it works! Good job you're done.
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
write an algebraic equation which could be used to solve the following problem. then find the solution: "A 40-inch rope is cut into three pieces so that the second piece is four times as long as the first and the third piece is three times as long as the first piece. Find the length of all three pieces."

...
first piece = x in
second piece = 4x
third = 3x
...
added they are 40 inches
x+4x+3x=40
8x=40
/8
x= 5 in first piece
second piece = 4x= 20 in
third piece = 3cx = 3*5 = 15 in
...
CHECK
15+20+5=40 in
...
m.ananth@hotmail.ca
Answer by vampirewitchreine(6)   (Show Source): You can put this solution on YOUR website!
Well lets start with the variable, and let x= the first piece. Now the second piece will now be 4x, and the third will be 3x.
Now let's plug this all into an equation
40=x+4x+3x
Now combine like terms
40=8x
Divide both sides by 8 and you have
5=x
Now substitute in
40=5+(4*5)+(3*5)
Which makes the first piece equal 5 inches, and the second piece (4x*5) equal 20 inches and the third piece (3x*5) equal 15.
This now makes the problem
40=5+20+15
And you have the final solution of
40=40
RELATED QUESTIONS
Two hundred meters of rope is used to mark off a rectangle (the dimensions are x meters... (answered by checkley75)
If x represents the number, then which of the following equations could be used to solve... (answered by checkley79)
Give an example of a real-life circumstance in which the concept of a rational algebraic... (answered by ikleyn,josgarithmetic)
A man bought a total of 80 feet of materials which are chain links and rope. A chain link (answered by Fombitz)
Create an example of a real-life word problem which can be solved using algebraic... (answered by ankor@dixie-net.com)
Please write the algebraic equation which can be used to find the exact solution of log... (answered by funmath)
Hi, I am trying to find a solution to the following equation: log 4x = log 8 + 1. My (answered by Personal Trainer DC)
Use ratios to write an equation that can be used to solve each of the following problems. (answered by quentin252)
What is the solution for this word problem: A rectangular garden is 10 feet by 16 feet.... (answered by glabow)