Question

Formulate a pair of linear equations in two variables “3 pens and 4 books
together cost Rs.50 whereas 5 pens and 3 books together cost Rs. 54”.​

Answer 1

Concept Used :-

Writing System of Linear Equations 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.

Let's solve the problem now!!

Let assume that

• Cost of 1 pen is Rs 'x'

• Cost of 1 book is Rs 'y'

According to first condition,

Cost of 3 pens and 4 books together is Rs 50.

So,

• Cost of 3 pens = 3x

and

• Cost of 4 books = 4y

Total cost = Rs 50

$\bf\implies \:3x + 4y = 50 - - - (1)$

According to second condition,

Cost of 5 pens and 3 books together is Rs 54.

So,

• Cost of 5 pens = 5x

and

• Cost of 3 books = 3y

Total cost = Rs 54

$\bf\implies \:5x + 3y = 54 - - - (2)$

$\begin{gathered}\begin{gathered}\bf\: Hence, \: pair \: of \: equations-\begin{cases} &\sf{3x + 4y = 50} \\ &\sf{5x + 3y = 54} \end{cases}\end{gathered}\end{gathered}$