# A pen and a pencil cost Rs.12. Three pencils and five pens cost Rs.56. Find the cost of one pen and one pencil.

Answer

Verified

362.7k+ views

Hint: Assume the cost of one pen and one pencil as some variable. Form simultaneous equations based on the data given and solve them.

Let the cost of one pen and one pencil is $Rs.x$ and $Rs.y$ respectively.

Then, according to the question, the cost of one pen and one pencil is Rs. 12. So, we have:

$

\Rightarrow x + y = 12, \\

\Rightarrow x = 12 - y .....(i) \\

$

Next, it is given that three pencils and five pens cost Rs.56. So, we have:

$ \Rightarrow 5x + 3y = 56 .....(ii)$

Putting the value of $x$ from equation $(i)$ into equation $(ii)$. We’ll get:

$

\Rightarrow 5\left( {12 - y} \right) + 3y = 56, \\

\Rightarrow 60 - 5y + 3y = 56, \\

\Rightarrow 2y = 4, \\

\Rightarrow y = 2 \\

$

Putting the value of $y$ in equation $(i)$ we’ll get:

$

\Rightarrow x = 12 - 2, \\

\Rightarrow x = 10 \\

$

Thus, the cost of one pen is Rs. 10 and that of one pencil is Rs. 2.

Note: We can solve simultaneous equations using the addition method also. In this, we try to make the coefficient of one of the variables same in both the equations by multiplying them with suitable constants. And then simply subtract any one equation from another to get a linear equation in one variable.

Let the cost of one pen and one pencil is $Rs.x$ and $Rs.y$ respectively.

Then, according to the question, the cost of one pen and one pencil is Rs. 12. So, we have:

$

\Rightarrow x + y = 12, \\

\Rightarrow x = 12 - y .....(i) \\

$

Next, it is given that three pencils and five pens cost Rs.56. So, we have:

$ \Rightarrow 5x + 3y = 56 .....(ii)$

Putting the value of $x$ from equation $(i)$ into equation $(ii)$. We’ll get:

$

\Rightarrow 5\left( {12 - y} \right) + 3y = 56, \\

\Rightarrow 60 - 5y + 3y = 56, \\

\Rightarrow 2y = 4, \\

\Rightarrow y = 2 \\

$

Putting the value of $y$ in equation $(i)$ we’ll get:

$

\Rightarrow x = 12 - 2, \\

\Rightarrow x = 10 \\

$

Thus, the cost of one pen is Rs. 10 and that of one pencil is Rs. 2.

Note: We can solve simultaneous equations using the addition method also. In this, we try to make the coefficient of one of the variables same in both the equations by multiplying them with suitable constants. And then simply subtract any one equation from another to get a linear equation in one variable.

Last updated date: 25th Sep 2023

•

Total views: 362.7k

•

Views today: 5.62k

Recently Updated Pages

What do you mean by public facilities

Paragraph on Friendship

Slogan on Noise Pollution

Disadvantages of Advertising

Prepare a Pocket Guide on First Aid for your School

10 Slogans on Save the Tiger

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

The equation xxx + 2 is satisfied when x is equal to class 10 maths CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Drive an expression for the electric field due to an class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

What is the past tense of read class 10 english CBSE