The coach of a cricket team buys 3 bats and 6 balls for ₹ 3900. Later, she buys another bat and 3 more balls of the same kind for ₹ 1300. Represent this situation algebraically and geometrically.
Solution:
Assuming the cost of one bat as ₹ x and the cost of one ball as ₹y, two linear equations can be formed for the situation given.
The cost of 3 bats and 6 balls is ₹ 3900. Mathematically:
3x + 6y = 3900
Also, the cost of 1 bat and 3 balls is ₹ 1300. Mathematically:
x + 3y = 1300
Algebraic representation where x and y are cost of bat and ball respectively.
3x + 6y = 3900 ---(1)
x + 3y = 1300 ---(2)
Therefore, the algebraic representation for equation (1) is:
3x + 6y = 3900
⇒ y = (1300 - x) / 2
And, the algebraic representation for equation (2 )is:
x + 3y = 1300
⇒ y = (1300 - x) / 3
Let us represent these equations graphically. For this, we need at least two solutions for each equation. We give these solutions in table shown below.
x |
500 |
900 |
y |
400 |
200 |
x |
400 |
700 |
y |
300 |
200 |
The graphical representation is as follows.
x axis:1 unit = ₹ 200, y axis: 1 unit = ₹ 100
☛ Check: Class 10 Maths NCERT Solutions Chapter 3
Video Solution:
The coach of a cricket team buys 3 bats and 6 balls for ₹ 3900. Later, she buys another bat and 3 more balls of the same kind for ₹ 1300. Represent this situation algebraically and geometrically
NCERT Solutions Class 10 Maths Chapter 3 Exercise 1.1 Question 2
Summary:
The coach of a cricket team buys 3 bats and 6 balls for ₹ 3900. Later, she buys another bat and 3 more balls of the same kind for ₹ 1300. This situation is algebraically and geometrically represented.
☛ Related Questions:
- The cost of 2 kg of apples and 1 kg of grapes on a day was found to be ₹ 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is ₹ 300. Represent the situation algebraically and geometrically.
- Form the pair of linear equations in the following problems and find their solutions graphically. (i) 10 students of Class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz. (ii) 5 pencils and 7 pens together cost ₹ 50, whereas 7 pencils and 5 pens together cost ₹ 46. Find the cost of one pencil and that of one pen.
- On comparing the ratios a1/a2 = b1/b2 = c1/c2, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident: i) 5x – 4y + 8 = 0 7x + 6y – 9 = 0 (ii) 9x + 3y + 12 = 0 18x + 6y + 24 = 0 (iii) 6x – 3y + 10 = 0 2x – y + 9 = 0
visual curriculum