b. Priya makes a noodle that is 456 feet long. The noodle breaks into 2 pieces One piece is 5 times as long as the other. How long are the 2 noodles? Explain or show your reasoning.

To determine the lengths of the two pieces of noodle that Priya made, let's break down the problem step by step. 1. **Understand the Problem:** - **Total length of the noodle:** 456 feet - **The noodle breaks into two pieces.** - **One piece is 5 times as long as the other piece.** 2. **Define Variables:** - Let’s denote the length of the shorter piece as **\( x \)**. - Then, the length of the longer piece will be **\( 5x \)** (since it's 5 times as long as the shorter piece). 3. **Set Up the Equation:** - The sum of the lengths of both pieces equals the total length of the original noodle. \[ x + 5x = 456 \] 4. **Simplify the Equation:** \[ 6x = 456 \] 5. **Solve for \( x \):** \[ x = \frac{456}{6} = 76 \text{ feet} \] 6. **Find the Length of the Longer Piece:** \[ 5x = 5 \times 76 = 380 \text{ feet} \] 7. **Check the Solution:** - **Shorter piece:** 76 feet - **Longer piece:** 380 feet - **Total:** \( 76 + 380 = 456 \) feet, which matches the original length. **Final Answer:** - **Shorter piece:** 76 feet - **Longer piece:** 380 feet