The highest score in an inning was frac{2}{9} | vedclass

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Question

(A) Let the total score be $x$.The highest score is $\frac{2}{9}x$.The remainder after the highest score is $x - \frac{2}{9}x = \frac{7}{9}x$.The next

Vedclass · Accepted Answer

$162$

Vedclass · Answer

(A) Let the total score be $x$.The highest score is $\frac{2}{9}x$.The remainder after the highest score is $x - \frac{2}{9}x = \frac{7}{9}x$.The next highest score is $\frac{2}{9}$ of the remainder,which is $\frac{2}{9} 	imes \frac{7}{9}x = \frac{14}{81}x$.The difference between these two scores is $8$ runs:$\frac{2}{9}x - \frac{14}{81}x = 8$.To subtract,find a common denominator $(81)$:$\frac{18}{81}x - \frac{14}{81}x = 8$.$\frac{4}{81}x = 8$.$x = 8 	imes \frac{81}{4} = 2 	imes 81 = 162$.Thus,the total score is $162$.

The highest score in an inning was $\frac{2}{9}$ of the total score and the next highest was $\frac{2}{9}$ of the remainder. These scores differ by $8$ runs. What was the total score in the innings?

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