Question

A Cricket player scored \[180\] runs in the first match and \[257\] runs the second match. Find the number of runs he should score in the third match so that the average of runs in the three matches be \[230\].

Answer 1

Hint:In average, we first add the sum of all the units given and then divide by the total number of unit given in that sum as given in the formula below:
Average of the units \[=\dfrac{\text{Sum of all the units}}{\text{Total number of units}}\]

Now to find the unknown unit, we take the unknown unit as \[x\] and the sum of other units and then equate it with the product of Average and total number of units.

Complete step by step solution:
The run scored by a cricket player in the first match is given as \[180\] runs.

The run scored by a cricket player in the second match is given as \[257\] runs.

The run scored by a cricket player in the third match is given as \[x\] runs.

The sum of all the runs scored in all the three matches are given as \[180+257+x\].

The average runs scored by the cricket player is given as \[230\] runs.

Applying the average formula for the runs scored by the cricket player is given as:
Average of the units \[=\dfrac{\text{Sum of all the units}}{\text{Total number of units}}\]
Placing the values in the formula of the average of the unit we get the value of the runs scored in the third match as:

\[\Rightarrow 230=\dfrac{180+257+x}{3}\]

\[\Rightarrow 230\times 3=180+257+x\]

\[\Rightarrow 437+x=690\]

\[\Rightarrow x=690-437\]

\[\Rightarrow x=253\]

Therefore, the run scored by him in the third match is equal to \[253\] runs.

Note:Students may go wrong if they try to divide the average value by all the units given. Dividing the average will not give the third match run value only product with the number of units will.