The ratio of thr number of apples to oranges to pears is 3:8:4. If there are 75 fruits altogether,  how many apples are there?

We are given the ratio of apples to oranges to pears as \( 3:8:4 \) and the total number of fruits is 75.

### Step 1: Represent the quantities with variables
Let the number of apples, oranges, and pears be represented by:
- \( 3x \) for apples,
- \( 8x \) for oranges,
- \( 4x \) for pears.

Here, \( x \) is the common multiplier for each of these quantities.

### Step 2: Set up the total equation
The total number of fruits is the sum of the apples, oranges, and pears:
\[
3x + 8x + 4x = 75
\]
Simplify the left-hand side:
\[
15x = 75
\]

### Step 3: Solve for \( x \)
Now, solve for \( x \) by dividing both sides by 15:
\[
x = \frac{75}{15} = 5
\]

### Step 4: Calculate the number of apples
Since the number of apples is \( 3x \), substitute \( x = 5 \) into this expression:
\[
3x = 3 \times 5 = 15
\]

Thus, there are **15 apples**.

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Would you like more details or have any questions?

Here are 5 related questions to explore:

1. If the ratio of apples to pears is maintained but the total is 150 fruits, how many apples would there be?
2. How many oranges are there in the original problem?
3. If 5 more apples are added, what would be the new ratio of apples to oranges to pears?
4. How would the total change if the ratio of oranges increased to 9 instead of 8?
5. What is the fraction of pears in the total number of fruits?

**Tip:** When solving ratio problems, always look for a common multiplier to easily relate the values to the total quantity.

The ratio of the number of apples to oranges to pears is 3:8:4. If there are 75 fruits altogether, how many apples are there?

Learn how to solve a ratio problem where the number of apples, oranges, and pears are in the ratio 3:8:4, and the total number of fruits is 75. This solution includes key algebraic concepts and step-by-step instructions. Suitable for students in Grades 6-8.

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