Question

a shopkeepper buys a number of books for RS.80.if the had bought 4 more books for the same amount.each book would have cost RS.1 less. how many books did he buy​

Answer 1

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

• A shopkeepper buys a number of books for Rs 80.

• If he had bought 4 more books for the same amount, each book would have cost Re 1 less.

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

• The number of books

Basic Concept Used :-

Writing System of Equation from Word Problems

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.

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

• Let us suppose that number of books = 'x'.

According to statement

• A shopkeepper buys a number of books for Rs 80.

So,

$\rm :\longmapsto\:Price \: of \: each \: book = \dfrac{80}{x} - - (1)$

According to statement,

• Number of books purchased = x + 4

• Amount spent = Rs 80

So,

$\rm :\longmapsto\:Price \: of \: each \: book = \dfrac{80}{x + 4} - - - (2)$

Now,

According to statement again,

$\rm :\longmapsto\:\dfrac{80}{x} - \dfrac{80}{x + 4} = 1$

$\rm :\longmapsto\:\dfrac{ \cancel{80x} + 320 - \cancel{80x}}{x(x + 4)} = 1$

$\rm :\longmapsto\: {x}^{2} + 4x - 320 = 0$

$\rm :\longmapsto\: {x}^{2} + 20x - 16x - 320 = 0$

$\rm :\longmapsto\:x(x + 20) - 16(x + 20) = 0$

$\rm :\longmapsto\:(x + 20)(x - 16) = 0$

$\rm :\implies\:x = 16 \: \: \: or \: \: \: x = - 20 \: \{rejected \}$

$\overbrace{ \underline { \boxed { \rm \therefore \: The \: number \: of \: books \: = \: 16}}}$