Let's walk through each given expression step-by-step to determine which one correctly represents the total amount of money spent by the three friends on tickets, food, and drink.
1. Expression 1: [tex]\((3+5) \times (5+3+6)\)[/tex]
- First, calculate the values inside the parentheses:
- [tex]\(3 + 5 = 8\)[/tex]
- [tex]\(5 + 3 + 6 = 14\)[/tex]
- Then, multiply the results of the two parentheses:
- [tex]\(8 \times 14 = 112\)[/tex]
- This expression evaluates to 112.
2. Expression 2: [tex]\((3 \times 5) \times (5+3+6)\)[/tex]
- First, calculate the values inside the parentheses:
- [tex]\(3 \times 5 = 15\)[/tex]
- [tex]\(5 + 3 + 6 = 14\)[/tex]
- Then, multiply the results of the two parentheses:
- [tex]\(15 \times 14 = 210\)[/tex]
- This expression evaluates to 210.
3. Expression 3: [tex]\((3 \times 5) + (5+3+6)\)[/tex]
- First, calculate the values inside the parentheses:
- [tex]\(3 \times 5 = 15\)[/tex]
- [tex]\(5 + 3 + 6 = 14\)[/tex]
- Then, add the results of the two parentheses:
- [tex]\(15 + 14 = 29\)[/tex]
- This expression evaluates to 29.
4. Expression 4: [tex]\((3+5) + (5 \times 3 \times 6)\)[/tex]
- First, calculate the values inside the parentheses:
- [tex]\(3 + 5 = 8\)[/tex]
- [tex]\(5 \times 3 = 15\)[/tex], then multiply by 6: [tex]\(15 \times 6 = 90\)[/tex]
- Then, add the results of the two parentheses:
- [tex]\(8 + 90 = 98\)[/tex]
- This expression evaluates to 98.
None of these options give us a direct value corresponding to the logical understanding except for the correct expression that encompasses the total money spent in the required logical context which evaluates to 112.
Therefore, the correct expression would be:
[tex]\[ (3+5) \times (5+3+6) \][/tex]
This expression reflects the total amount of money spent correctly.
