Find the best tutors and institutes for Class 10 Tuition
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
Chapters in CBSE - Class 10 Mathematics
Top Tutors who teach Pair of linear equations in two variable
Top Tutor
Doddakallasandra, Bangalore
11 yrs of
Exp
3 students
14 hrs of classes completed
500
per hour
Tutor's home
Have taught in school for 10th grade students.
Top Tutor
Mira Road, Mira-Bhayandar
10 yrs of
Exp
7 students
84 hrs of classes completed
600
per hour
Student's Home
Tutor's home
Math and physics teacher. Expert in cbse education and assessment patten. Been an cbse examiner for 5 continuous years. Aware of the curriculum of ssc, icse and cbse grade 7-10 math and physics. Tutoring since 2006 and been quite successful in giving results.
Super Tutor
Kodambakkam, Chennai
15 yrs of
Exp
57 students
4103 hrs of classes completed
800
per hour
Online Classes
With a decade of experience in teaching mathematics, physics, and chemistry for students from grades 8 through 12 across CBSE, IB, and ICSE boards, I offer a comprehensive educational approach that caters to a diverse range of curricula and learning needs. My academic background includes a BE and an MBA, equipping me with both technical and managerial skills that enhance my teaching methodology. Throughout my career, I have specialized in home tutoring, where I have developed a personalized approach to education that focuses on each student's unique needs and strengths. My sessions are designed to be interactive and engaging, fostering a learning environment where students feel supported and motivated. I conduct both online and offline classes, each lasting one hour, and utilize a variety of teaching tools to facilitate learning. I employ a whiteboard to visually explain concepts and provide question papers to help students practice and prepare for their exams. This hands-on approach ensures that students not only understand theoretical concepts but also develop problem-solving skills and confidence in their subjects. My commitment to delivering high-quality education and my extensive experience make me well-suited to guide students through their academic journey, helping them achieve their full potential in mathematics, physics, and chemistry.
Shri Seshadri sir was able to break the jinx of my son not learning indefinitely, with his experience in smoothly sliding into a routine with such interactive, yet nonchalant transition for my son's education. Thankyou sir, thankyou UrbanPro.
Super Tutor
Basaveshwara Nagar, Bangalore
12 yrs of
Exp
14 students
3497 hrs of classes completed
800
per hour
Online Classes
With over 15 years of dedicated teaching experience, I am an accomplished and qualified educator specializing in Spoken English, Math, Science, Social Science, and Kannada Language. My expertise extends across various educational boards, including CBSE, ICSE, and state boards. Passionate about unraveling the mysteries of mathematical problems and chemical equations. I have garnered recognition with the prestigious Best Teacher Award for orchestrating state-level Science exams. Having contributed my skills to the esteemed MaxMuller Public School in Bangalore, I am committed to fostering a nurturing and inspiring learning environment. Join me on this educational journey where knowledge meets enthusiasm!
For the last one and a half months, it has been going well; it is the first review in the initial stage. Again, I will review as a class exam, the results come up, but the teaching to date has been very good.
Super Tutor
Pandri, Raipur
4 yrs of
Exp
10 students
2687 hrs of classes completed
575
per hour
Online Classes
Hello, my name is Atulya Kumar. I have completed my studies at IIT(ISM)_Dhanbad and I am currently pursuing a PhD at NIT-Rourkela. With a degree in engineering, I am dedicated to teaching. Since 2019, I have been teaching physics to JEE, NEET, and Class XI & XII board students. I take great pride in sharing that my students have achieved exceptional results, with some clearing NEET 2022 with an AIR of 2513 and NEET 2023 with an AIR of 1702. Additionally, many of my students have scored above the 98th percentile in JEE Mains 2023. Teaching physics is a personal challenge for me. I strive to create a comfortable learning environment where students can fully grasp the concepts and apply them effectively during examinations, resulting in excellent marks and ranks.
Find more Tutor for Pair of linear equations in two variable in your City
- Bangalore Mathematics Tutors
- Delhi Mathematics Tutors
- Chennai Mathematics Tutors
- Gurgaon Mathematics Tutors
- Noida Mathematics Tutors
- Hyderabad Mathematics Tutors
- Mumbai Mathematics Tutors
- Ghaziabad Mathematics Tutors
- Chandigarh Mathematics Tutors
- Pune Mathematics Tutors
- Jaipur Mathematics Tutors
- Surat Mathematics Tutors
Download free CBSE - Class 10 Mathematics Pair of linear equations in two variable EXERCISE 3.2 worksheets
Download Now
