a 50 foot length of rope was cut into two pieces. the first piece is 5 feet more than twice the second. what are the lengths of the two pieces of rope?
short piece --- x
longer piece --- 2x + 5
solve:
x + 2x+5 = 50
take it from here.
X=15
Let's assume the length of the second piece of the rope is x feet. According to the information given, the first piece will be 5 feet more than twice the second piece.
Length of the first piece = 2x + 5 feet
We know that the sum of the lengths of the two pieces should be equal to the original length of the rope, which is 50 feet.
So, x + (2x + 5) = 50
Now, let's solve this equation to find the value of x:
3x + 5 = 50
Subtracting 5 from both sides:
3x = 45
Dividing both sides by 3:
x = 15
Therefore, the length of the second piece of the rope is 15 feet.
To find the length of the first piece:
First piece = 2x + 5
= 2(15) + 5
= 30 + 5
= 35
Hence, the lengths of the two pieces of rope are 15 feet and 35 feet.
To solve this problem, let's assign variables to the lengths of the two pieces of rope. Let's call the length of the second piece "x."
According to the problem, the length of the first piece is 5 feet more than twice the second piece. This can be expressed as "2x + 5."
Given that the total length of the rope is 50 feet, we can set up an equation:
x + (2x + 5) = 50
Now, let's solve the equation:
Combine like terms:
3x + 5 = 50
Subtract 5 from both sides:
3x = 45
Divide both sides by 3:
x = 15
Therefore, the length of the second piece of rope, represented by "x," is 15 feet.
To find the length of the first piece, substitute the value of x back into the expression 2x + 5:
2(15) + 5 = 30 + 5 = 35
Hence, the lengths of the two pieces of rope are 15 feet and 35 feet.