At a baseball game, a vender sold a combined total of 204 sodas and hot dogs. The number of sodas sold was three times the number of hot dogs sold. Find the number of sodas and the number of hot dogs sold.

Let the number of hot dogs sold be \( x \), and the number of sodas sold be \( 3x \) (since the number of sodas is three times the number of hot dogs).

The total number of sodas and hot dogs sold is 204, so we can set up the equation:

\[
x + 3x = 204
\]

Simplifying:

\[
4x = 204
\]

Now, divide both sides by 4:

\[
x = \frac{204}{4} = 51
\]

So, the number of hot dogs sold is 51. Since the number of sodas sold is three times the number of hot dogs:

\[
\text{Number of sodas} = 3 \times 51 = 153
\]

Thus, the vendor sold 51 hot dogs and 153 sodas.

Would you like further details or explanations on any part?

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Here are 5 questions related to this problem:
1. What if the number of sodas was four times the number of hot dogs sold?
2. How would the total change if 20 more hot dogs were sold?
3. If 75 more sodas were sold, what would be the new total?
4. Can you express the relationship between sodas and hot dogs as a proportion?
5. What would happen if the total number of items sold increased to 250?

**Tip**: In word problems, translating the relationships into algebraic expressions is key to solving them effectively.

At a baseball game, a vendor sold a combined total of 204 sodas and hot dogs. The number of sodas sold was three times the number of hot dogs sold. Find the number of sodas and the number of hot dogs sold.

Learn how to solve a linear equation problem where the total number of sodas and hot dogs sold is 204, and the number of sodas is three times the number of hot dogs. This solution involves basic algebra and is ideal for students in Grades 6-8.

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