This season,
How many games have been played in India?
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Yes sir you are right and you did great that explained every step
Let the number of games played in India be x . Then 3 2 x + 5 2 ( 4 9 − x ) = 2 6 or x = 2 4
Sir you are right and you did great that you take only one variable
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One variable is enough for solving this problem. There is no need to get stuck in a jungle of variables.
Virat's team won at home = 3 2 of their home games.
Virat's team won away from home = 5 2 of their away from games.
Virat's team won in total = 26 games out of total 49 games.
3 2 of their home games + 5 2 of their away from games = 4 9 2 6 of their total games.
Now assume total they played games in India are x and total they played games away from India are y .
So 3 2 x + 5 2 y = 2 6
Now we don't want fractions because we hate fractions and we love whole numbers so multiply both sides by 15.
So 15 *( 3 2 x + 5 2 y ) = 15 * 26
= 3 1 5 ∗ 2 x + 5 1 5 ∗ 2 y
= 10x + 6y = 390
= 5x + 3y = 195
And we know that x + y = 49 So 3x + 3y = 147
Now compare this two equations: 3x + 3y = 147 and 5x + 3y = 195
So know subtract (5x + 3y ) - ( 3x + 3y ) = (195 - 147)
= 2x = 48
x = 24
And we have x as no games played in India.
So we know x + y = 49
Then y will be 25.
So matches played in INDIA are x which means "24".
(Optional: Games played far from their home are y which means "25" )
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Let the number of games played in and out of India be x and y respectively. Then we have:
⎩ ⎨ ⎧ 3 2 x + 5 2 y = 2 6 x + y = 4 9 . . . ( 1 ) . . . ( 2 ) ⟹ 2 5 × ( 1 ) − ( 2 ) : 3 2 x = 1 6 ⟹ x = 2 4