Algebraic expressions & sequences · Ages 12–13
Situations into algebra
Work it once with real numbers, then swap in the letter.
How to do it
Method
Work it once with real numbers, then swap in the letter
$8 each, 3 books: 8 × 3; n books: 8n dollars
Another way
Start from the relationship
Total = price × quantity = 8 × n = 8n
In full
First ask: with real numbers, how would I work this out? A book costs $8, so 3 books cost 8 × 3 dollars; change the 3 to n and n books cost 8n dollars. Then use the relationships: total = price × quantity, change = money paid − total, distance = speed × time, and a perimeter is the sum of the sides. The gap between two people's ages never changes, and someone aged x is x + 5 in 5 years. Or start from the relationship itself: write 'total = price × quantity' and fill in what you know. Both ways give the same answer. Keep the units the same: x hours 20 minutes is 60x + 20 minutes.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
x hours 35 minutes = (x + 35) minutes; with x = 7, that is minutes.
Fill in each blank
Show the answer and working
Answer: 60, 455
One hour has 60 minutes, so x hours have 60x. Put in the number: 60 × 7 + 35 = 455.
Example 2
A rectangle is x cm long, and its width is 2 cm less. Width = (x − ) cm; perimeter = (x − ) cm.
Fill in each blank
Show the answer and working
Answer: 2, 4, 4
Perimeter = x + x + (x − 2) + (x − 2) = 4x − 4.
Example 3
A car goes at v km an hour for t hours, then at 70 km an hour for 5 hours. How many km is that in all?
- A. vt + 75
- B. v + t + 350
- C. (v + 70)(t + 5)
- D. vt + 350
Choose the right answer
Show the answer and working
Answer: D. vt + 350
Distance = speed × time: vt for the first part, 70 × 5 = 350 for the second: vt + 350.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.One eraser costs $18. How many dollars do n erasers cost?
- A. n − 18
- B. n18
- C. 18n
- D. 18 + n
Choose the right answer
Answer:
2.x hours 5 minutes = (x + 5) minutes; with x = 8, that is minutes.
Fill in each blank
Answer:
3.A rectangle is x cm long, and its width is 9 cm less. Width = (x − ) cm; perimeter = (x − ) cm.
Fill in each blank
Answer:
4.Pens cost $12 each and notebooks $8 each. x pens and y notebooks cost 12x + 8y dollars.
True or false?
Answer:
5.A car goes at v km an hour for t hours, then at 50 km an hour for 2 hours. How many km is that in all?
- A. vt + 52
- B. (v + 50)(t + 2)
- C. v + t + 100
- D. vt + 100
Choose the right answer
Answer:
All the answers
- 1. C. 18n
- 2. 60, 485
- 3. 9, 4, 18
- 4. True
- 5. D. vt + 100
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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