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Q3(iii):
Form the pair of linear equations for the following problems and find their solution by substitution method. (iii) 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.
Solution :
Given:
1. The cost of 7 bats and 6 balls is ₹ 3800.
2. The cost of 3 bats and 5 balls is ₹ 1750.
To Find:
The cost of one bat and the cost of one ball.
Step 1: Defining Variables
Let the cost of one bat be $x$ and the cost of one ball be $y$.
Step 2: Formulating the Linear Equations
Based on the given information, we can construct the following system of linear equations:
Equation (1): $7x + 6y = 3800$
Equation (2): $3x + 5y = 1750$
Step 3: Applying the Substitution Method
From Equation (2), express $x$ in terms of $y$:
$3x = 1750 - 5y$
$x = \frac{1750 - 5y}{3}$ --- (Equation 3)
Step 4: Substituting Equation (3) into Equation (1)
Substitute the value of $x$ from Equation (3) into Equation (1):
$7\left(\frac{1750 - 5y}{3}\right) + 6y = 3800$
Multiply the entire equation by 3 to eliminate the denominator:
$7(1750 - 5y) + 18y = 3800 \times 3$
$12250 - 35y + 18y = 11400$
Combine the $y$ terms:
$12250 - 17y = 11400$
Isolate the variable $y$:
$-17y = 11400 - 12250$
$-17y = -850$
$y = \frac{-850}{-17}$
$y = 50$
Step 5: Finding the value of $x$
Substitute $y = 50$ into Equation (3):
$x = \frac{1750 - 5(50)}{3}$
$x = \frac{1750 - 250}{3}$
$x = \frac{1500}{3}$
$x = 500$
Step 6: Verification
Check the values in Equation (1): $7(500) + 6(50) = 3500 + 300 = 3800$. (Correct)
Check the values in Equation (2): $3(500) + 5(50) = 1500 + 250 = 1750$. (Correct)
Final Answer: The cost of one bat is ₹ 500 and the cost of one ball is ₹ 50.
More Questions from Class 10 Mathematics Pair of linear equations in two variable EXERCISE 3.2
- Q1(i): Solve the following pair of linear equations by the substitution method. (i) x + y = 14; x – y = 4
- Q1(ii): Solve the following pair of linear equations by the substitution method. (ii) s – t = 3; $\frac{s}{3} + \frac{t}{2} = 6$
- Q1(iii): Solve the following pair of linear equations by the substitution method. (iii) 3x – y = 3; 9x – 3y = 9
- Q1(iv): Solve the following pair of linear equations by the substitution method. (iv) 0.2x + 0.3y = 1.3; 0.4x + 0.5y = 2.3
- Q1(v): Solve the following pair of linear equations by the substitution method. (v) $\sqrt{2}x + \sqrt{3}y = 0$; $\sqrt{3}x - \sqrt{8}y = 0$
- Q1(vi): Solve the following pair of linear equations by the substitution method. (vi) $\frac{3x}{2} - \frac{5y}{3} = -2$; $\frac{x}{3} + \frac{y}{2} = \frac{13}{6}$
- Q2: Solve 2x + 3y = 11 and 2x – 4y = – 24 and hence find the value of ‘$m$’ for which y = mx + 3.
- Q3(i): Form the pair of linear equations for the following problems and find their solution by substitution method. (i) The difference between two numbers is 26 and one number is three times the other. Find them.
- Q3(ii): Form the pair of linear equations for the following problems and find their solution by substitution method. (ii) The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.
- Q3(iv): Form the pair of linear equations for the following problems and find their solution by substitution method. (iv) The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is ` 105 and for a journey of 15 km, the charge paid is ` 155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km?
- Q3(v): Form the pair of linear equations for the following problems and find their solution by substitution method. (v) A fraction becomes $\frac{9}{11}$, if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes $\frac{5}{6}$. Find the fraction.
- Q3(vi): Form the pair of linear equations for the following problems and find their solution by substitution method. (vi) Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?
CBSE Solutions for Class 10 Mathematics Pair of linear equations in two variable
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