India's cricket team batman's are tiger in india

Algebra Level 2

This season,

  • Virats's "cricket"🏏 team has won {INDIAN cricket team} 2 3 \frac{2}{3} of their home games😊 (games played in India),
  • but just 2 5 \frac{2}{5} of their away games 😩 (games played out of India).
  • In total, Virat's team has won 26 games out of 49 games they have played.

How many games have been played in India?

25 24 26 49

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3 solutions

Chew-Seong Cheong
Oct 15, 2019

Let the number of games played in and out of India be x x and y y respectively. Then we have:

{ 2 3 x + 2 5 y = 26 . . . ( 1 ) x + y = 49 . . . ( 2 ) \begin{cases} \dfrac 23 x + \dfrac 25 y = 26 & ...(1) \\ x + y = 49 & ...(2) \end{cases} 5 2 × ( 1 ) ( 2 ) : 2 3 x = 16 x = 24 \implies \dfrac 52 \times (1) - (2): \ \dfrac 23 x = 16 \implies x = \boxed{24}

Yes sir you are right and you did great that explained every step

Harsh Chaudhari - 1 year, 7 months ago

Let the number of games played in India be x x . Then 2 x 3 + 2 ( 49 x ) 5 = 26 \dfrac{2x}{3}+\dfrac{2(49-x)}{5}=26 or x = 24 x=\boxed {24}

Sir you are right and you did great that you take only one variable

Harsh Chaudhari - 1 year, 7 months ago

Log in to reply

One variable is enough for solving this problem. There is no need to get stuck in a jungle of variables.

A Former Brilliant Member - 1 year, 7 months ago
Harsh Chaudhari
Oct 16, 2019

Virat's team won at home = 2 3 \frac{2}{3} of their home games.

Virat's team won away from home = 2 5 \frac{2}{5} of their away from games.

Virat's team won in total = 26 games out of total 49 games.

2 3 \frac{2}{3} of their home games + 2 5 \frac{2}{5} of their away from games = 26 49 \frac{26}{49} of their total games.

Now assume total they played games in India are x x and total they played games away from India are y y .

So 2 x 3 \frac{2x}{3} + 2 y 5 \frac{2y}{5} = 26 26

Now we don't want fractions because we hate fractions and we love whole numbers so multiply both sides by 15.

So 15 *( 2 x 3 \frac{2x}{3} + 2 y 5 \frac{2y}{5} ) = 15 * 26

= 15 2 x 3 \frac{15 * 2x}{3} + 15 2 y 5 \frac{15 * 2y}{5}

= 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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