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

Algebra ->  Equations -> 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      Log On


   



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) About Me  (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) About Me  (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) About Me  (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