Carla cuts a 70 - inch piece of ribbon into 2 pieces. If the first piece is 5 inches more than one - fourth as long as the second piece, how long is the longer piece of ribbon?

Answer

To solve the problem, we need to determine the lengths of the two pieces of ribbon that Carla cuts from the 70-inch ribbon. Let's break it down step by step.

### Step 1: Define the Variables
Let the length of the second piece of ribbon be \( x \) inches.

### Step 2: Express the First Piece in Terms of \( x \)
According to the problem, the first piece is 5 inches more than one-fourth the length of the second piece. Therefore, we can express the first piece as:
\[ \text{First Piece} = \frac{x}{4} + 5 \]

### Step 3: Set Up the Equation
Since the total length of the ribbon is 70 inches, we can set up the equation:
\[ \text{First Piece} + \text{Second Piece} = 70 \]
Substituting the expressions we have:
\[ \left(\frac{x}{4} + 5\right) + x = 70 \]

### Step 4: Simplify the Equation
Combine like terms:
\[ \frac{x}{4} + x + 5 = 70 \]
To combine \( \frac{x}{4} \) and \( x \), convert \( x \) into a fraction:
\[ \frac{x}{4} + \frac{4x}{4} + 5 = 70 \]
This simplifies to:
\[ \frac{5x}{4} + 5 = 70 \]

### Step 5: Isolate the Variable
Subtract 5 from both sides:
\[ \frac{5x}{4} = 70 - 5 \]
\[ \frac{5x}{4} = 65 \]

### Step 6: Solve for \( x \)
Multiply both sides by 4 to eliminate the fraction:
\[ 5x = 65 \times 4 \]
\[ 5x = 260 \]
Now, divide by 5:
\[ x = \frac{260}{5} \]
\[ x = 52 \]

### Step 7: Find the Length of the First Piece
Now that we have \( x \), which is the length of the second piece, we can find the length of the first piece:
\[ \text{First Piece} = \frac{52}{4} + 5 = 13 + 5 = 18 \]

### Step 8: Determine the Longer Piece
Now we have:
- Length of the first piece = 18 inches
- Length of the second piece = 52 inches

The longer piece of ribbon is:
\[ \text{Longer Piece} = 52 \text{ inches} \]

### Final Answer
The longer piece of ribbon is **52 inches**.