A basket contains only apples and oranges, and the ratio of apples to oranges is \( 9: 7 \). If there are 128 pieces of fruit in the basket, how many are oranges?

To determine the number of oranges in the basket, let's break down the problem step by step. 1. **Understand the Ratio:** - The ratio of apples to oranges is \( 9:7 \). - This means for every 9 apples, there are 7 oranges. 2. **Set Up the Equation:** - Let \( k \) be the common multiplier for the ratio. - Number of apples = \( 9k \) - Number of oranges = \( 7k \) 3. **Total Fruits:** - According to the problem, the total number of fruits is 128. - So, \( 9k + 7k = 16k = 128 \) 4. **Solve for \( k \):** \[ 16k = 128 \\ k = \frac{128}{16} \\ k = 8 \] 5. **Find the Number of Oranges:** \[ \text{Number of oranges} = 7k = 7 \times 8 = 56 \] **Answer:** There are **56 oranges** in the basket.