Question

Jane was measuring the length of ribbons,A,B and C.The total length of A and B is 151cm.The total length of B and C is 147cm.The total length of A and C is 130cm.What is the length of ribbon A?

Answer 1

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:

1. \(a + b = 151\) (Equation 1)
2. \(b + c = 147\) (Equation 2)
3. \(a + c = 130\) (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.