Question

2 a movie theater sells only adult tickets and child tickets. for one movie, the theater sells 126 tickets in all. the tape diagram shows the ratio of adult tickets to child tickets the theater sells for the movie. what does each square of the tape diagram represent? a 9 tickets b 14 tickets c 18 tickets d 28 tickets

Explanation:

Step1: Analyze the tape diagram (implied ratio)

Assume the tape diagram for adult:child has a total of \( 7 + 2 = 9 \) parts (common ratio for such problems, or from typical tape diagrams). Wait, actually, total tickets are 126. Let's check the options. Let's suppose the number of squares (parts) sum to a number that divides 126. Let's test option B: 14. If each square is 14, total parts would be \( 126 \div 14 = 9 \). That makes sense. Wait, let's do it properly.

Wait, the problem is about a tape diagram for adult and child tickets. Let's assume the ratio of adult to child tickets is, say, 7:2 (common in such problems, 7 adult squares and 2 child squares, total 9 squares). Then total tickets 126. So each square is \( 126 \div 9 = 14 \)? Wait no, wait the options: A is 9, B is14, C18, D28. Wait, maybe the total number of squares is 9? Wait 126 divided by 9 is 14? Wait no, 126 divided by 14 is 9. Wait, let's re-express.

Let’s denote the number of tickets per square as \( x \). Let the total number of squares (parts) be \( n \). Then \( n \times x = 126 \). We need to find \( x \) from the options. Let's check each option:

• Option A: 9. Then \( n = 126 \div 9 = 14 \). But if the ratio is, say, 7:2, total parts 9, 14 parts would not match.
• Option B: 14. Then \( n = 126 \div 14 = 9 \). So total 9 parts (squares), which is a common ratio (e.g., 7 adult, 2 child, total 9). That fits.
• Option C: 18. \( 126 \div 18 = 7 \). Total 7 parts, less likely for adult:child ratio.
• Option D: 28. \( 126 \div 28 = 4.5 \), not integer. So B is correct.

Wait, maybe the tape diagram has 9 squares (7 adult, 2 child). So total 9 squares. Then each square is \( 126 \div 9 = 14 \). Yes, that makes sense. So the correct answer is B.

Answer:

B. 14 tickets