A set A consists of integers 27, 28, 30, 32 a | vedclass

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(A) The original sum of the elements in set $A$ is $27 + 28 + 30 + 32 + 33 = 150$.The original average of set $A$ is $\frac{150}{5} = 30$.When integer

Vedclass · Accepted Answer

$84$

Vedclass · Answer

(A) The original sum of the elements in set $A$ is $27 + 28 + 30 + 32 + 33 = 150$.The original average of set $A$ is $\frac{150}{5} = 30$.When integer $K$ is included,the new sum becomes $150 + K$ and the number of elements becomes $6$.The new average is given as an increase of $30\%$ over the original average,which is $30 + (0.30 	imes 30) = 30 + 9 = 39$.Setting up the equation for the new average: $\frac{150 + K}{6} = 39$.Multiplying both sides by $6$,we get $150 + K = 234$.Solving for $K$,we get $K = 234 - 150 = 84$.

$A$ set $A$ consists of integers $27, 28, 30, 32$ and $33$. If an integer $K$ is included,the average of set $A$ will increase by $30\%$. What is the value of integer $K$?

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