Question
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?
Ask by Schofield Hodgson. in Canada
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
There are 56 oranges in the basket.
Solution
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.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To solve the problem, we start by defining the number of apples and oranges based on the given ratio of \( 9: 7 \). If we let the number of apples be \( 9x \) and the number of oranges be \( 7x \), we can set up the equation: \[ 9x + 7x = 128 \] This simplifies to: \[ 16x = 128 \] Dividing both sides by 16 gives us: \[ x = 8 \] Now we can find the number of oranges: \[ 7x = 7 \times 8 = 56 \] So, there are 56 oranges in the basket. In summary, the basket contains 56 oranges and \( 9x = 72 \) apples for a total of 128 fruits.
