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To solve this problem, let's define the number of each type of can in terms of \( x \), which is the number of cans of beans:

1. **Beans**: There are \( x \) cans.
2. **Soup**: Twice as many as beans, so there are \( 2x \) cans of soup.
3. **Tomato paste**: Half as many as beans, so there are \( \frac{x}{2} \) cans of tomato paste.

### Total Cans Calculation
The total number of cans is the sum of these three quantities:
\[
x + 2x + \frac{x}{2}
\]

To simplify, we add the terms:
\[
x + 2x + \frac{x}{2} = \frac{2x + 4x + x}{2} = \frac{7x}{2}
\]

Thus, the total number of cans in the pantry is \( \frac{7x}{2} \).

### Determining Possible Values
Since the total number of cans must be a whole number, \( \frac{7x}{2} \) must be an integer. This requires that \( x \) be an even number.

Now, let’s check each option to see which could be the total number of cans:

#### Checking the Options
We solve for \( x \) in each case by setting \( \frac{7x}{2} = \) (each option):

1. **If \( \frac{7x}{2} = 6 \):**
   \[
   7x = 12 \Rightarrow x = \frac{12}{7} \quad (\text{not an integer})
   \]

2. **If \( \frac{7x}{2} = 7 \):**
   \[
   7x = 14 \Rightarrow x = 2 \quad (\text{integer})
   \]

3. **If \( \frac{7x}{2} = 36 \):**
   \[
   7x = 72 \Rightarrow x = \frac{72}{7} \quad (\text{not an integer})
   \]

4. **If \( \frac{7x}{2} = 45 \):**
   \[
   7x = 90 \Rightarrow x = \frac{90}{7} \quad (\text{not an integer})
   \]

5. **If \( \frac{7x}{2} = 63 \):**
   \[
   7x = 126 \Rightarrow x = 18 \quad (\text{integer})
   \]

### Conclusion
The values of the total cans that satisfy the conditions are:
- **7**
- **63**

Would you like a detailed breakdown of each calculation step, or do you have any further questions?

### Related Questions:
1. How would the answer change if there were three times as many cans of soup as beans?
2. What would the solution be if there were one-third as many cans of tomato paste as beans?
3. If the pantry had additional cans, how would this affect the total calculation?
4. Can we determine the values of \( x \) for other possible total numbers of cans not listed here?
5. How can we generalize this problem for other pantry combinations?

**Tip**: Always check if expressions in problems with fractions simplify to whole numbers, as this can be a quick way to eliminate certain answers.

A pantry holds x cans of beans, twice as many cans of soup, and half as many cans of tomato paste as there are cans of beans. If there are no other cans in the pantry, which of the following could be the total number of cans in the pantry? Indicate two such numbers.

Learn how to determine the possible total number of cans in a pantry with algebraic expressions. Given x cans of beans, twice as many cans of soup, and half as many cans of tomato paste, this problem explores finding whole number solutions for total cans in the pantry.

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