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# Question of the Day (hard-ish)

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In leading their basketball team to victory, Kylie and Shaniqua were the top 2 scorers in the championship game. Using the following clues, determine how many points each girl scored:

• If you subtract 2 times Kylie's points from 3 times Shaniqua's points, the difference is less than 6
• Shaniqua scored at least as many points as nine more than 1/4 of Kylie's points
• Kylie scored fewer then 20 points

Remember that in basketball you can only score whole number of points.

Jan 17, 2019
edited by Guest  Jan 17, 2019

#1
+1

Let x = Shaniqua's points

Let y = Kylie's points

If you subtract 2 times Kylie's points from 3 times Shaniqua's points, the difference is less than 6

This translates as

3x - 2y < 6

Shaniqua scored at least as many points as nine more than 1/4 of Kylie's points

This translates as

x ≥   y/4 +  9

Kylie scored fewer then 20 points

This translates as

y < 20

Note that Kylie's number of points must be divisible by 4

And since she scoes < 20, she must have scored either 16, 12, 8 or 4    points

But....you can test for yourself.....there are no integer solutions

As close as we can be is if she scores 16

Then as few as Shaniqua could score is  16/4 + 9   =  13

But....these values make the first inequality     3(13) - 2(16)  =  7

But...the constraint is that this is < 6

So.....no integer solutions exist   Jan 17, 2019
#3
+1

Note however.....if we drop the provision that Kylie's points be evenly divisible by 4.....at least one integer solution exists

(14, 19)

This satisfies

3(14)  - 2(19)   =  5      which is  < 6

14  ≥  19 /4 +  9

14  ≥   13.75

And

y < 20

19 < 20   CPhill  Jan 17, 2019