Question

The total cost of 3 tables and 2 chairs is 1850rs . If a table costs 75rs more than a chair, find the Price of each.

Answer 1

$let \: rs \: x \: be \: the \: cost \:$

Then, the cost of the table is Rs(x+75).

Now,

$3(x + 75) + 2x = 1850$

$3x + 225 + 2x = 1850$

$5x = 1625$

$x = \frac{1625}{5} = 325$

cost of the chair.

Rs 325; cost of the table.

(325+75)=Rs 400.

Answer 2

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

Given that,

↝ The total cost of 3 tables and 2 chairs is Rs 1850

Let us assume that,

↝ Cost of 1 table be Rs x.

↝ Cost of 1 chair be Rs y.

So,

↝ Cost of 3 tables = Rs 3x

↝ Cost of 2 chairs = Rs 2y

↝ So, Total cost = Rs 1850

$\rm \implies\:\boxed{ \tt{ \: 3x + 2y = 1850 \: }} - - - - - (1)$

Again, Given that

↝ A table costs Rs 75 more than a chair.

$\rm :\longmapsto\:\boxed{ \tt{ \: x = 75 + y}} - - - (2)$

So, on substituting equation (2) in equation (1), we get

$\rm :\longmapsto\:3(75 + y) + 2y = 1850$

$\rm :\longmapsto\:225 + 3y + 2y = 1850$

$\rm :\longmapsto\: 5y = 1850 - 225$

$\rm :\longmapsto\: 5y = 1625$

$\rm \implies\:\boxed{ \tt{ \: y = 325 \: }} - - - - (3)$

Substituting y = 525 in equation (2), we get

$\rm :\longmapsto\:x = 325 + 75$

$\rm \implies\:\boxed{ \tt{ \: x = 400 \: }} - - - - (4)$

Hence,

• Cost of 1 table is Rs 400

• Cost of 1 chair is Rs 325.

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Basic Concept Used :-

Writing Systems of Linear 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.