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.

SHOW YOUR WORK!

Guest 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

CPhill Jan 17, 2019