Answer
Verified
440.4k+ views
Hint: We can take the cost of ball pen as one variable and cost of fountain pen as another variable. By reading the given statement, we can understand that half of the cost of a fountain pen minus 5 gives the cost of a ball pen. We get the required equation by writing the relation in terms to two variables and simplifying.
Complete step by step answer:
We are given two objects, a ball pen and fountain pen. We can assign any two variables to the cost of ball pen and cost of fountain pen
Let \[{\text{x = }}\] cost of fountain pen
And let \[{\text{y = }}\] cost of ball pen
According to the question, half of the cost of fountain pen minus 5 gives the cost of a ball pen. Writing this in terms of variables, we get,
${\text{y = }}\dfrac{{\text{x}}}{{\text{2}}}{\text{ - 5}}$
Rearranging the equation, we get
$
{\text{y + 5 = }}\dfrac{{\text{x}}}{{\text{2}}} \\
{\text{2y + 10 = x}} \\
$
Therefore, the required linear equation in 2 variables is ${\text{x = 2y + 10}}$.
Note: As the variable is not mentioned, we can use any variable. We must make sure that it is clearly written what each of the variables used refers to, and we should not mix them up. In this problem we convert a statement into a mathematical equation. This method of solving is known as mathematical modeling. Using mathematical modeling we can form equations from a statement and we can solve for the variable if the number of equations formed is greater than the number of variables, we can solve for the variables. The number of variables used must be minimum to avoid errors. We must read and understand the given statement completely to form the equations.
Complete step by step answer:
We are given two objects, a ball pen and fountain pen. We can assign any two variables to the cost of ball pen and cost of fountain pen
Let \[{\text{x = }}\] cost of fountain pen
And let \[{\text{y = }}\] cost of ball pen
According to the question, half of the cost of fountain pen minus 5 gives the cost of a ball pen. Writing this in terms of variables, we get,
${\text{y = }}\dfrac{{\text{x}}}{{\text{2}}}{\text{ - 5}}$
Rearranging the equation, we get
$
{\text{y + 5 = }}\dfrac{{\text{x}}}{{\text{2}}} \\
{\text{2y + 10 = x}} \\
$
Therefore, the required linear equation in 2 variables is ${\text{x = 2y + 10}}$.
Note: As the variable is not mentioned, we can use any variable. We must make sure that it is clearly written what each of the variables used refers to, and we should not mix them up. In this problem we convert a statement into a mathematical equation. This method of solving is known as mathematical modeling. Using mathematical modeling we can form equations from a statement and we can solve for the variable if the number of equations formed is greater than the number of variables, we can solve for the variables. The number of variables used must be minimum to avoid errors. We must read and understand the given statement completely to form the equations.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Differentiate between homogeneous and heterogeneous class 12 chemistry 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
Which are the Top 10 Largest Countries of the World?
Give 10 examples for herbs , shrubs , climbers , creepers
10 examples of evaporation in daily life with explanations
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Why is there a time difference of about 5 hours between class 10 social science CBSE