how do you slove this problem a rope is 72 feet long is cut into two pieces the longer piece is 3 feet than twice the shorter piece. How long is each piece ???
shorter piece---x
longer piece --- 2x+3
solve
x + 2x+3 = 72
x=23
To solve this problem, we can use algebra. Let's assign variables to represent the lengths of the two pieces of rope.
Let x be the length of the shorter piece of rope.
According to the problem, the longer piece is 3 feet longer than twice the length of the shorter piece. So, the longer piece would be 2x + 3.
We know that the sum of the lengths of the two pieces is 72 feet.
Therefore, the equation will be x + (2x + 3) = 72.
Now, let's solve this equation to find the value of x, which will represent the length of the shorter piece of rope.
x + 2x + 3 = 72
3x + 3 = 72
3x = 72 - 3
3x = 69
x = 69/3
x = 23
So, the length of the shorter piece of rope is 23 feet.
To find the length of the longer piece, we substitute the value of x back into the equation for the longer piece:
2x + 3 = 2(23) + 3 = 46 + 3 = 49
Therefore, the length of the longer piece of rope is 49 feet.