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In ten-pin bowling, the highest possible score in a single game is 300. At one point in the bowling season, Fred F Stone had an average score of 177. In his next game he obtained a score of 199, which caused his average to increase to. 178. After one more game Fred would like his average to be 183. Is it possible for Fred

Respuesta :

Let, number of games played is n and sum of their points are x.

So, [tex]177=\dfrac{x}{n}[/tex]    

Now, In his next game he obtained a score of 199, which caused his average to increase to 178.

[tex]178=\dfrac{x+199}{n+1}[/tex]

Now equations are :

x = 177n    ...1)

x + 199 = 178( n + 1 )

x = 178n - 21  ...2)

Solving eq 1 and 2 , we get :

x = 3717 and n = 21 .

Now, new average is 183.

Let, point scored in last game is y.

So,

[tex]183 =\dfrac{x+y}{n+1+1}\\\\183 = \dfrac{3717+y}{23}\\\\y = 183\times 23 - 3717\\\\y=492[/tex]

He required 492 points which is greater than the maximum i.e 300.

Therefore, it is not possible for Fred.

Hence, this is the required solution.

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