Worked solution
Cinema tickets: one price per age category
A cinema sells tickets at three different prices, depending on the age of the customers. The age categories are under 16 years, between 16 and 65 years, and over 65 years.
Three groups of people A, B and C go to the cinema on the same day.
The numbers in each age category for each group, together with the total cost of the tickets for each group, are given in the following table.
| Group | Under 16 years | Between 16 and 65 years | Over 65 years | Total cost |
|---|---|---|---|---|
| A | 9 | 6 | 4 | $162.03 |
| B | 7 | 5 | 3 | $128.36 |
| C | 10 | 4 | 5 | $158.50 |
Write down and solve equations to find the cost of a ticket for each of the age categories. marks
[2012/I/1]
CJC · Review Problems · Question 1
Answer
Under 16: $7.65; between 16 and 65: $9.85; over 65: $8.52.
Form the system
Let be ticket prices in dollars for under 16, between 16 and 65, and over 65 respectively. The three groups give Each coefficient counts tickets in its age category.
Solve and interpret
The source uses a GC to solve the system: . Ticket costs are therefore $7.65, $9.85 and $8.52 respectively. Substitution gives all three original totals, so the prices satisfy every group, not just one pair of equations.
Common mistakes
Use the same age-category order in every row of the coefficient system.
Solution notes
Also printed as Review 1 in both CJC Linear Equations lecture copies: question PDF page 13 / printed 173; answer PDF 15 / Student printed 175, Teacher visible footer 15 (extracted 175). Compared in evidence/review-cjc-linear-equations-lecture.md; the repeated asks, tables and marks retain this existing identity.
Both lecture answer keys label the first price as <65 years. The question and its first table column say under 16; the correct first category is under 16 at $7.65. The mistaken source label is retained in the lecture native transcription.