The ratio of tomatoes to red apples is 2:5. If there are 20 tomatoes, how many red apples are there?
Understand the Problem
The question is asking us to solve a word problem involving ratios. It states that the ratio of tomatoes to red apples is 2:5 and provides the number of tomatoes (20). We need to determine how many red apples correspond to this number of tomatoes based on the given ratio.
Answer
The number of red apples is \( 50 \).
Answer for screen readers
The number of red apples is given by ( x = 50 ).
Steps to Solve
- Identify the ratio and quantities
The ratio of tomatoes to red apples is given as 2:5. This means for every 2 tomatoes, there are 5 red apples.
- Set up a proportion
Let ( x ) be the number of red apples. We can set up the relationship as a proportion based on the ratio:
$$ \frac{20 \text{ tomatoes}}{x \text{ red apples}} = \frac{2 \text{ tomatoes}}{5 \text{ red apples}} $$
- Cross-multiply to solve for ( x )
Cross-multiplying gives us:
$$ 20 \cdot 5 = 2 \cdot x $$
This simplifies to:
$$ 100 = 2x $$
- Solve for ( x )
Now, divide both sides by 2:
$$ x = \frac{100}{2} $$
Calculating that will give us the number of red apples.
- Calculate the final answer
Upon dividing, we find:
$$ x = 50 $$
Thus, there are 50 red apples corresponding to the 20 tomatoes.
The number of red apples is given by ( x = 50 ).
More Information
In this problem, we used the concept of ratios and proportions to find the corresponding number of red apples based on the given number of tomatoes. Understanding ratios can help in various real-life situations, such as cooking, mixing ingredients, or financial calculations.
Tips
- A common mistake is confusing the order of the ratio. Be sure to maintain the correct order (tomatoes to red apples).
- Another error could be incorrect cross-multiplication. Always double-check your multiplication steps to avoid simple arithmetic errors.
AI-generated content may contain errors. Please verify critical information
