Answer:
Step-by-step explanation:
Given the question
A rope is 24 feet long. It is cut into two pieces such that one piece is half the length of the other. Find the lengths of the two pieces of rope.
Options
The stated solution is correct (lengths of 16 feet and 8 feet).
Based on the way the variable is defined, the equation should be x + 2x = 24.
The equation is written correctly, but there is an error in solving the equation.
The way the variable is defined, and because x=16, the longer piece of rope would be 32 feet, which is not possible.
2
Let the length of one piece be x (shorter piece) and the other be y.
If the rope is cut into two pieces and 24ft long, then;
x+y = 24.......... 1
If one piece is half the length of the other, then x = y/2..... 2
substitute equation 2 into 1
y/2 + y = 24
take the LCM
y+2y/2 = 24
3y/2 = 24
cross multiply
3y = 48
Divide both sides by 3;
3y/3 = 48/3
y = 16 feet
Since x = y/2
x = 16/2
x = 8 feet
Based on the calculation above, I can conclude that;
- The student stated solution is correct (lengths of 16 feet and 8 feet)
- The way the variable is defined, and because x=16, the longer piece of rope would be 32 feet, which is not possible.
- Based on the way the variable is defined, the equation should be x + 2x = 24.
