The pattern
Algebra basics
Use a letter for an unknown number and work with what it means.
A letter standing in for an unknown number needs matching to its part of the story: which part repeats for every ticket, and which part is paid only once, such as a booking fee. Multiplication by a letter drops its usual sign, so four times x is written 4x, the letter straight after the number. Once the story is written this way, a given value can replace the letter to work out one price.
How to spot it
A story with a repeated cost and a fixed fee, written as an expression like 4x + 4, points here. So does a value for x to substitute in.
Common mistake
Children swap the two numbers round, using the fixed fee as the price per ticket and the price per ticket as the fixed fee.
10 worked solutions
Standard
- Algebra — interpret Tickets cost $6 each, with a booking fee of $5. The total cost in dollars is 6x + 5. What does x represent?
- Algebra — interpret Tickets cost $4 each, with a booking fee of $4. The total cost in dollars is 4x + 4. What does x represent?
- Algebra — represent Let x be the number of pens bought. Each pen costs $6. Express the total cost in dollars using x.
- Algebra — represent Let x be the number of pens bought. Each pen costs $4. Express the total cost in dollars using x.
- Algebra — simplify Simplify 6x + 5x + 8.
- Algebra — simplify Simplify 4x + 4x + 6.
- Algebra — solve Solve 6x + 5 = 53.
- Algebra — solve Solve 4x + 4 = 28.
- Algebra — substitute Find 6x + 5 when x = 8.
- Algebra — substitute Find 4x + 4 when x = 6.
All the problem patterns → · the revision list
The 33 problem patterns
All 33 patterns, one to a page — the 19 behind Primary 5 and 6 word problems, and the skills the younger years are built on. The bar model, how to spot it in the question, and the mistake children make. A booklet you can print. Free.
A PDF, and a note when new solutions go up.