Let's denote the lengths of ribbons A, B, and C as follows:
- Length of ribbon A = \(a\)
- Length of ribbon B = \(b\)
- Length of ribbon C = \(c\)
From the problem, we have the following equations based on the total lengths of the ribbons:
- \(a + b = 151\) (Equation 1)
- \(b + c = 147\) (Equation 2)
- \(a + c = 130\) (Equation 3)
We can solve these equations step-by-step.
First, we can express \(b\) and \(c\) in terms of \(a\) using the equations:
From Equation 1, we can express \(b\): \[ b = 151 - a \]
Substituting this value for \(b\) into Equation 2:
\[ (151 - a) + c = 147 \] \[ c = 147 - 151 + a \] \[ c = a - 4 \quad (Equation 4) \]
Now, substitute this expression for \(c\) into Equation 3:
\[ a + (a - 4) = 130 \] \[ 2a - 4 = 130 \] \[ 2a = 130 + 4 \] \[ 2a = 134 \] \[ a = 67 \]
Thus, the length of ribbon A is \( \boxed{67} \) cm.
To find the lengths of ribbons B and C for verification: From Equation 1: \[ b = 151 - a = 151 - 67 = 84 \text{ cm} \] From Equation 4: \[ c = a - 4 = 67 - 4 = 63 \text{ cm} \]
Now we can check all conditions:
- \(a + b = 67 + 84 = 151\) (correct)
- \(b + c = 84 + 63 = 147\) (correct)
- \(a + c = 67 + 63 = 130\) (correct)
Therefore, all equations are satisfied, confirming that the length of ribbon A is \( \boxed{67} \) cm.