Form the pair of linear equations for the following problems and find their solution by the substitution method.
The coach of a cricket team buys $7$ bats and $6$ balls for ₹ $3800$. Later,she buys $3$ bats and $5$ balls for ₹ $1750$. Find the cost of each bat and each ball.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(A) Let the cost of a bat be $x$ and the cost of a ball be $y$.
According to the given information:
$7x + 6y = 3800$ $...(1)$
$3x + 5y = 1750$ $...(2)$
From equation $(1)$,we express $y$ in terms of $x$:
$6y = 3800 - 7x$
$y = \frac{3800 - 7x}{6}$ $...(3)$
Substituting this value of $y$ into equation $(2)$:
$3x + 5\left(\frac{3800 - 7x}{6}\right) = 1750$
Multiply the entire equation by $6$ to simplify:
$18x + 5(3800 - 7x) = 10500$
$18x + 19000 - 35x = 10500$
$-17x = 10500 - 19000$
$-17x = -8500$
$x = 500$
Now,substitute $x = 500$ into equation $(3)$:
$y = \frac{3800 - 7(500)}{6}$
$y = \frac{3800 - 3500}{6}$
$y = \frac{300}{6} = 50$
Therefore,the cost of one bat is ₹ $500$ and the cost of one ball is ₹ $50$.

Explore More

Similar Questions

Solve the following pair of linear equations:
$px + qy = p - q$
$qx - py = p + q$

Difficult
View Solution

Form the pair of linear equations for the following problem,and find their solutions (if they exist) by the elimination method:
If we add $1$ to the numerator and subtract $1$ from the denominator,a fraction reduces to $1$. It becomes $\frac{1}{2}$ if we only add $1$ to the denominator. What is the fraction?

Difficult
View Solution

Solve the following pair of linear equations by the elimination method and the substitution method:
$3x + 4y = 10$ and $2x - 2y = 2$

On comparing the ratios $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}}$,find out whether the following pair of linear equations are consistent or inconsistent:
$\frac{4}{3} x + 2 y = 8$; $2 x + 3 y = 12$

On comparing the ratios $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}},$ find out whether the following pair of linear equations are consistent or inconsistent.
$5x - 3y = 11$; $-10x + 6y = -22$

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo