Introduction to Linear Polynomials | Exercise 2.3

Question 1

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.
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Solution
Understand the Question
  • Initial amount in savings account = ₹500.
  • Amount added every month (pocket money) = ₹150.
  • For any month nn, the total money is the initial deposit plus nn times the monthly pocket money.
  • We calculate the amount from the second month onwards and express the general pattern as a linear expression in terms of nn.

Step 1 · Calculate Monthly Amounts

Given initial savings =₹500= \text{₹}500 and monthly pocket money =₹150= \text{₹}150.Diagram 1

At the end of the 2nd month:

=500+(2×150)=500+300=800\begin{aligned} &= 500 + (2 \times 150) \\ &= 500 + 300 \\ &= 800 \end{aligned}

At the end of the 3rd month:

=500+(3×150)=500+450=950\begin{aligned} &= 500 + (3 \times 150) \\ &= 500 + 450 \\ &= 950 \end{aligned}

At the end of the 4th month:

=500+(4×150)=500+600=1100\begin{aligned} &= 500 + (4 \times 150) \\ &= 500 + 600 \\ &= 1100 \end{aligned}

Step 2 · Find the Linear Expression

Let AnA_n represent the total amount at the end of the nthn^{\text{th}} month.

An=Initial amount+(Number of months×Monthly pocket money)=500+(n×150)=150n+500\begin{aligned} A_n &= \text{Initial amount} + (\text{Number of months} \times \text{Monthly pocket money}) \\ &= 500 + (n \times 150) \\ &= 150n + 500 \end{aligned}
Answer

At the end of the 2nd, 3rd, and 4th months, she will have ₹800, ₹950, and ₹1100 respectively.

The linear expression for the nthn^{\text{th}} month is: An=150n+500A_n = 150n + 500

Common Mistakes
  • Omitting Initial Savings: Forgetting to add the initial deposit ₹500 and incorrectly writing the linear expression as An=150nA_n = 150n.
  • Index Confusion: Using (n−1)(n - 1) instead of nn, forgetting that pocket money is received in each of the nn months.

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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