A cord is cut into two pieces of different lengths. The sum of the two lengths is 12 centimeters, and the difference between the two lengths is 4 centimeters. Find the lengths of the two pieces of cord.
x + y = 12
x - y = 4
Add the two equations together to eliminate the y.
2x = 16 x = 8 so y = 4
Check these values in the original equations.
Let's represent the lengths of the two pieces of cord as x and y.
According to the given information, the sum of the two lengths is 12 centimeters:
x + y = 12 ----(1)
Also, the difference between the two lengths is 4 centimeters:
x - y = 4 ----(2)
To solve the system of equations (1) and (2), we can use the method of substitution or elimination.
Let's solve it using the method of substitution:
From equation (2), we can rearrange it to express x in terms of y:
x = y + 4 ----(3)
Substituting equation (3) into equation (1), we get:
(y + 4) + y = 12
2y + 4 = 12
2y = 12 - 4
2y = 8
y = 8 / 2
y = 4
Substituting the value of y back into equation (3), we can find x:
x = 4 + 4
x = 8
Therefore, the lengths of the two pieces of cord are 8 centimeters and 4 centimeters.
Let's call the length of one piece of cord x centimeters and the length of the other piece y centimeters.
According to the given information, we can form two equations:
Equation 1: x + y = 12 (the sum of the two lengths is 12 centimeters)
Equation 2: x - y = 4 (the difference between the two lengths is 4 centimeters)
To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution:
From Equation 2, we can express x in terms of y:
x = y + 4
Substitute this value of x into Equation 1:
(y + 4) + y = 12
Combine like terms:
2y + 4 = 12
Subtract 4 from both sides:
2y = 8
Divide by 2:
y = 4
Now substitute the value of y back into the expression for x:
x = 4 + 4
x = 8
Therefore, the lengths of the two pieces of cord are 8 centimeters and 4 centimeters, respectively.