Introduction to Linear Polynomials | Exercise 2.3

Question 5

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.

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Solution
Understand the Question
  • Total pages in the book =500= 500.
  • Sarita reads 2020 pages every day, so after nn days, the number of pages read is 20n20n.
  • The number of pages remaining is obtained by subtracting the pages read from the total pages: Pages left=500−20n\text{Pages left} = 500 - 20n.
  • To find the pages left after 1515 days, evaluate the pattern at n=15n = 15.

Step 1 · Calculate Pages Left After 15 Days

Given:

  • Total pages=500\text{Total pages} = 500
  • Pages read per day=20\text{Pages read per day} = 20Diagram 1

Calculate the pages read in 1515 days:

Pages read in 15 days=20×15=300\begin{aligned} \text{Pages read in 15 days} &= 20 \times 15 \\[0.6em] &= 300 \end{aligned}

Calculate the pages left:

Pages left=500−300=200\begin{aligned} \text{Pages left} &= 500 - 300 \\[0.6em] &= 200 \end{aligned}

Step 2 · Express as a Linear Pattern

Let PnP_n represent the number of pages left after nn days.

Pn=Total pages−Pages read in n days=500−20n\begin{aligned} P_n &= \text{Total pages} - \text{Pages read in } n \text{ days} \\[0.6em] &= 500 - 20n \end{aligned}
Answer

Pages left after 15 days =200= 200

Linear pattern: Pn=500−20nP_n = 500 - 20n

Common Mistakes
  • Adding Instead of Subtracting: Writing 500+20n500 + 20n instead of 500−20n500 - 20n. Since pages are being read, the number of remaining pages decreases.
  • Confusing Pages Read with Pages Left: Stating 20n20n as the linear pattern instead of 500−20n500 - 20n.

More questions in Exercise 2.3

Q1

Solve the following:

  1. A student has ₹500 in her savings bank account. She gets ₹150 every month as pocket money. How much money will she have at the end of every month from the second month onwards? Find a linear expression to represent the amount she will have in the nthn^{\text{th}} month.
Q2

A rally starts with 120 members. Each hour, 9 members drop out of the group. How many members will remain after 1,2,3,…1, 2, 3, \dots hours? Find a linear expression to represent the number of members at the end of the nthn^{\text{th}} hour.

Q3

Suppose the length of a rectangle is 13 cm13\text{ cm}. Find the area if the breadth is (i) 12 cm12\text{ cm}, (ii) 10 cm10\text{ cm}, (iii) 8 cm8\text{ cm}. Find the linear pattern representing the area of the rectangle.

Q4

Suppose the length of a rectangular box is 7 cm7\text{ cm} and breadth is 11 cm11\text{ cm}. Find the volume if the height is (i) 5 cm5\text{ cm}, (ii) 9 cm9\text{ cm}, (iii) 13 cm13\text{ cm}. Find the linear pattern representing the volume of the rectangular box.

Q5

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.

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