The problem in the image gives a ratio of apples to grapes to oranges as $2:4:1$, and mentions that there are 20 grapes in total.

Step 1: Understand the Ratio

The given ratio is $2 : 4 : 1$, which means for every:

• 2 parts of apples
• 4 parts of grapes
• 1 part of oranges

Step 2: Set Up the Relationship

Since there are 4 parts of grapes and the total number of grapes is 20, we can determine the "value of one part" by dividing the total number of grapes by the number of parts: $\frac{20 \text{ grapes}}{4 \text{ parts}} = 5 \text{ grapes per part}$

Step 3: Find the Number of Apples and Oranges

Now that we know each part equals 5 pieces of fruit:

• Apples: $2 \times 5 = 10$ apples
• Oranges: $1 \times 5 = 5$ oranges

Step 4: Calculate the Total Number of Items

To find the total number of items in the bowl, sum all the apples, grapes, and oranges: $10 \text{ apples} + 20 \text{ grapes} + 5 \text{ oranges} = 35 \text{ total items}$

Conclusion:

• The number of apples is 10.
• The total number of items in the bowl is 35.

Would you like a more detailed explanation on any of the steps? Here are five related questions to expand on this problem:

1. How would the total change if there were 30 grapes instead of 20?
2. What would the ratio need to be if there were 15 apples instead of 10?
3. How do you find the number of oranges if the total number of fruits is unknown?
4. Can you express the total number of fruits algebraically based on the parts?
5. How does changing the ratio impact the total count of items?

Tip: Always use the given ratio to determine the "value of one part" when solving these types of problems.