Sarita is reading a book of 500 pages. She reads 20 pages every day. How many pages will be left after 15 days? Express this as a linear pattern.
Answer: Pages left after n days = 500 − 20n. After 15 days: 500 − 300 = 200 pages.
Step-by-step solution
Given: Book of 500 pages; 20 pages read every day
To find: Pages left after 15 days, and the linear pattern
To find: Pages left after 15 days, and the linear pattern
Idea: Each day the number of pages left falls by the same 20. After n days, 20n pages have been read.
- Pages left: 480, 460, 440, 420, … after 1, 2, 3, 4, … days (20 fewer each day).1 mark
- Pages left after n days = 500 − 20n (a linear pattern).1 mark
- After 15 days: 500 − 20 × 15 = 500 − 300 = 200 pages.1 mark
200 pages will be left after 15 days; the linear pattern is 500 − 20n pages after n days.
Check: 15 days × 20 pages = 300 pages read; 300 + 200 = 500 ✓.
Answer to write in the exam
Pages left after 1, 2, 3, … days: 480, 460, 440, …
Pages left after n days = 500 − 20n
After 15 days: 500 − 20(15) = 500 − 300
∴ 200 pages will be left
Common mistakes that cost marks
- Giving 300 (pages read) when the question asks for pages left.
- Writing the pattern as 500n − 20 or 20n − 500.
- Forgetting that the pattern decreases: writing 500 + 20n.
How this can come in the exam
MCQ (1 mark)
Sarita finishes the 500-page book (20 pages a day) in
- 20 days
- 25 days
- 30 days
- 50 days
Show answer
(B) 25 days
500 − 20n = 0 ⇒ n = 25.
Short answer (2 marks)
Arif has 360 pages to read and reads 24 pages a day. Write the pages left after d days and find when 120 pages are left.
Show answer
360 − 24d (1 mark). 360 − 24d = 120 ⇒ d = 10 days (1 mark).Try one yourself
A book has 640 pages; Neha reads 32 pages a day. How many pages are left after 12 days?
Show answer
640 − 32 × 12 = 640 − 384 = 256 pages.
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