Question

The students of class VIII donated a total of ₹ 2209 towards a charity. Each student donated
an amount equal to the number of students in the class. How many students are there in this
class? Show all the steps clearly.

Answer 1

$\red{\large\underline{\sf{Given- }}}$

The students of class VIII donated a total of ₹ 2209 towards a charity. Each student donated an amount equal to the number of students in the class.

$\green{\large\underline{\sf{To\:Find - }}}$

Number of students in the class.

$\blue{\large\underline{\sf{Solution-}}}$

Given that

• The students of class VIII donated a total of ₹ 2209 towards a charity. Each student donated an amount equal to the number of students in the class.

Let assume that

• Number of students in class be x

So,

• Amount donated by each student = ₹ x

According to statement,

$\rm :\longmapsto\:x \times x = 2209$

$\rm :\longmapsto\: {x}^{2} = 2209$

$\rm \implies\:x = \sqrt{2209}$

Now, we have to find the square root of 2209 using Long Division Method.

$\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\:47 \:\:}}}\\ {\underline{\sf{4}}}& {\sf{\:\:2209 \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: \: \: \: \: \: 16 \:    \:  \:  \:  \:  \: \:\:}} \\ {\underline{\sf{87}}}& {\sf{\:\: \: \: \: \: 609\:  \:    \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: 609 \:  \:\:}} \\ {\underline{\sf{}}}& {\sf{\: \:   0\:\:}}{\sf{}}&{\sf{\:\:\:\:}}\end{array}\end{gathered}$

Hence,

$\rm \implies\:x = 47$

So, it means

• Number of students in class = 47

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Basic Concept Used :-

Writing System of Equation from Word Problem.

1. Understand the problem.

• Understand all the words used in stating the problem.

• Understand what you are asked to find.

2. Translate the problem to an equation.

• Assign a variable (or variables) to represent the unknown.

• Clearly state what the variable represents.

3. Carry out the plan and solve the problem.

Answer 2

Answer:

47

Step-by-step explanation:

${x}^{2} = 2209$

$x = \sqrt{2209}$

$x = 47$