a 3 1/2 foot piece of rope is cut into two pieces. one of these pieces is 8 inches shorter than the other. how long are the pieces?
Let x = the shorter piece. Solve for x
x + x + 8 = 42
2x = 42 - 8
2x = 34
x = ?
A rope 15m long was cut into pieces 1/2m long to teach tying of knots to scouts. how many pieces were cut ?
To find the lengths of the two pieces of rope, we can set up an equation. Let's represent the length of one piece as x and the length of the other piece as y.
Given that the total length of the rope is 3 1/2 feet, we need to convert this into inches. Since there are 12 inches in 1 foot, we have:
3 1/2 feet = (3 * 12) inches + (1/2 * 12) inches = 36 inches + 6 inches = 42 inches
Now, we are told that one of the pieces is 8 inches shorter than the other. This can be represented as:
x = y + 8
Also, we know that the sum of the lengths of the two pieces is equal to the total length of the rope. This can be represented as:
x + y = 42
Now we have a system of equations:
x = y + 8
x + y = 42
We can solve this system using substitution or elimination.
Using substitution:
Substitute the value of x from the first equation into the second equation:
(y + 8) + y = 42
2y + 8 = 42
2y = 34
y = 17
Now substitute the value of y back into the first equation to find x:
x = 17 + 8
x = 25
Therefore, one piece of the rope is 25 inches long and the other piece is 17 inches long.