The length of rope P is three times the length of rope Q. After 10 cm of rope is cut from rope P and rope Q respectively, the length of rope P is four times the length of rope Q. Calculate the original length, in cm, of rope P before it is cut.
p = 3q, so
3q-10 = 4(q-10)
solve for q, and then p=3q.
Let's assume the original length of rope Q is x cm.
According to the given information, the length of rope P is three times the length of rope Q, so the original length of rope P is 3x cm.
After 10 cm of rope is cut from each rope, the length of rope P becomes 3x - 10 cm and the length of rope Q becomes x - 10 cm.
It is also given that after cutting, the length of rope P is four times the length of rope Q, so we can write the equation:
3x - 10 = 4(x - 10)
Let's solve this equation to find the value of x:
3x - 10 = 4x - 40
Subtracting 3x from both sides:
-10 = x - 40
Adding 40 to both sides:
30 = x
Therefore, the original length of rope Q is 30 cm.
To find the original length of rope P, we substitute the value of x in the equation for the original length of rope P:
3x = 3(30) = 90 cm
Hence, the original length of rope P before it was cut is 90 cm.
Let's call the original length of rope Q as x cm.
According to the given information, the length of rope P is three times the length of rope Q. Therefore, the length of rope P is 3x cm.
After 10 cm is cut from each rope, the length of rope P becomes four times the length of rope Q.
So, the new length of rope P is (3x - 10) cm, and the new length of rope Q is (x - 10) cm.
According to the second condition, the new length of rope P is four times the new length of rope Q. So we can write the equation:
3x - 10 = 4(x - 10)
Now let's solve this equation to find the value of x.
Distribute the 4 on the right side of the equation:
3x - 10 = 4x - 40
Move the variables to one side:
3x - 4x = -40 + 10
-x = -30
Divide both sides by -1:
x = 30
Therefore, the original length of rope Q is 30 cm.
Now we can find the original length of rope P:
P = 3x = 3 * 30 = 90
So, the original length of rope P before it is cut is 90 cm.