Question

In her last basketball game, Jackie scored 36 points. These points raised the average number of points that she scored per game from 20 to 21. To raise this average to 22.5 points, how many points must Jackie score in her next game?

Options :-
• 46.5
• 42.5
• 38.5
• None of the above

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Answer 1

SOLUTION

GIVEN

In her last basketball game, Jackie scored 36 points. These points raised the average number of points that she scored per game from 20 to 21.

TO CHOOSE THE CORRECT OPTION

To raise this average to 22.5 points, the points must Jackie score in her next game

• 46.5

• 42.5

• 38.5

• None of the above

EVALUATION

Let n be the number of games when the average was 20

So (n+1) is the number of games when the average was 21

Now it is given that 36 points raised the average number of points that she scored per game from 20 to 21.

So by the given condition

$\sf{21(n + 1) = 20n + 36}$

$\sf{ \implies \: 21n + 21 = 20n + 36}$

$\sf{ \implies \: n =15}$

So 16 is the number of games when the average was 21

In 16 games total number of points

= 16 × 21

= 336

Now in order to raise the average to 22.5 in next game ( 17 game) total number of points in 17 games will be

= 17 × 22.5

= 382.5

Hence the required number of points must Jackie score in her next game

= 382.5 - 336

= 46.5

FINAL ANSWER

The correct option is 46.5

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