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.
Last updated date: 18th Mar 2023
•
Total views: 306.3k
•
Views today: 8.85k
Answer
306.3k+ 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.
Recently Updated Pages
Paulings electronegativity values for elements are class 11 chemistry CBSE

For a particle executing simple harmonic motion the class 11 physics CBSE

Does Nichrome have high resistance class 12 physics CBSE

The function f satisfies the functional equation 3fleft class 12 maths JEE_Main

Write a letter to the Principal of your school to plead class 10 english CBSE

Look at the handout below Write a letter to the organizers class 11 english CBSE

Trending doubts
What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

Name the Largest and the Smallest Cell in the Human Body ?
