The coach of a cricket team buys 7 bats and 6 balls for Rs. 3800. Later, he buys 3 bats and 5 balls for Rs. 1750. Find the cost of each bat and each ball.
Last updated date: 15th Mar 2023
•
Total views: 305.1k
•
Views today: 5.85k
Answer
305.1k+ views
Hint: Assume a variable x which represents the cost of each bat and assume a variable y which represents the cost of each ball. Apply the two situations that are given in the question to get two equations. These two equations can be solved together to get the value of two variables.
In this question, we are given that 7 bats and 6 balls had cost Rs. 3800 and 3 bats and 5 balls had cost Rs. 1750. We are required to find the cost for each bat and each ball.
Let us assume that each bat had a cost of Rs. x and each ball had a cost of Rs. y.
It is given that 7 bats and 6 balls had cost Rs. 3800. So, we can write,
$7x+6y=3800............\left( 1 \right)$
Also, it is given that 3 bats and 5 balls had cost Rs. 1750. So, we can write,
$3x+5y=1750...........\left( 2 \right)$
By solving these two equations simultaneously, we can find x and y. Multiplying equation $\left( 1 \right)$ by 3 and equation $\left( 2 \right)$ by 7, we get,
$21x+18y=11400............\left( 3 \right)$
$21x+35y=12250............\left( 4 \right)$
Subtracting the above two equations, we get,
$\begin{align}
& \left( 21x+35y \right)-\left( 21x+18y \right)=12250-11400 \\
& \Rightarrow 17y=850 \\
& \Rightarrow y=50 \\
\end{align}$
Substituting y=50 in equation $\left( 1 \right)$, we get,
$\begin{align}
& 7x+6\left( 50 \right)=3800 \\
& \Rightarrow 7x+300=3800 \\
& \Rightarrow 7x=3500 \\
& \Rightarrow x=500 \\
\end{align}$
Hence, the cost of each bat is equal to Rs. 500 and each ball is equal to Rs. 50.
Note: To check whether we have got the correct answer or not, just substitute the obtained values of x and y in any of the equation $\left( 1 \right)$ and equation $\left( 2 \right)$. If the obtained value of x and y satisfies the equation, we have obtained a correct value of x and y.
In this question, we are given that 7 bats and 6 balls had cost Rs. 3800 and 3 bats and 5 balls had cost Rs. 1750. We are required to find the cost for each bat and each ball.
Let us assume that each bat had a cost of Rs. x and each ball had a cost of Rs. y.
It is given that 7 bats and 6 balls had cost Rs. 3800. So, we can write,
$7x+6y=3800............\left( 1 \right)$
Also, it is given that 3 bats and 5 balls had cost Rs. 1750. So, we can write,
$3x+5y=1750...........\left( 2 \right)$
By solving these two equations simultaneously, we can find x and y. Multiplying equation $\left( 1 \right)$ by 3 and equation $\left( 2 \right)$ by 7, we get,
$21x+18y=11400............\left( 3 \right)$
$21x+35y=12250............\left( 4 \right)$
Subtracting the above two equations, we get,
$\begin{align}
& \left( 21x+35y \right)-\left( 21x+18y \right)=12250-11400 \\
& \Rightarrow 17y=850 \\
& \Rightarrow y=50 \\
\end{align}$
Substituting y=50 in equation $\left( 1 \right)$, we get,
$\begin{align}
& 7x+6\left( 50 \right)=3800 \\
& \Rightarrow 7x+300=3800 \\
& \Rightarrow 7x=3500 \\
& \Rightarrow x=500 \\
\end{align}$
Hence, the cost of each bat is equal to Rs. 500 and each ball is equal to Rs. 50.
Note: To check whether we have got the correct answer or not, just substitute the obtained values of x and y in any of the equation $\left( 1 \right)$ and equation $\left( 2 \right)$. If the obtained value of x and y satisfies the equation, we have obtained a correct value of x and y.
Recently Updated Pages
If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts
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

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

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE
