Problem of the Week

Step 1:

What I know:

-         Jay Fann teaches 7^th grade and has 30 students

-         He determined that 21 students out of 30 students love baseball

-         If every student is present, the probability of asking a baseball fan was 7/10 vs. 3/10

-         1 baseball fan (at least) & 1 non-baseball fan (at least) were absent

-         More than half of his class was present

-         The probability of asking a baseball fan a question ¾

What I want to know:

-         Is there enough information to determine how many students were there that morning?

Options

a)     If yes, how many students were absent?

b)     If no, why not?

Step 2:

Strategies (Let’s make a plan!):

In order to overcome this situation, I need to first do a layout of all the numbers 1-30 and cross out any that don’t apply to the terms above.

Step 3:

Carrying out the plan:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30.

Since all the possible amounts are above half. The numbers 1-15 must be eliminated.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30.

All the possible numbers must be able to be divisible by 2, so numbers 17, 19, 21, 23, 25, 27, and 29.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30.

All the possible numbers must be able to be divisible by 4, so the numbers 18, 22, 26 and 30.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30.

If 16 students are present:

¾ of 16=12 so 12/16 are baseball fans and 4/16 (1/4) are not fans.

If 20 students are present:

¾ of 20=15 so 15/20 are baseball fans and 5/20 (1/4) are not fans.

If 24 students are present:

¾ of 24=18 so 18/24 are baseball fans and 6/24 (1/4) are not fans.

If 28 students are present:

¾ of 28= 21 so 21/28 are baseball fans and 7/28 (1/4) are not fans.

Step 4:

Check your work (Let’s check to see if I’m right):

16/4=4 J

20/4=5 J

24/4=6 J

28/4=8 J

18/2=9 J

22/2=11 J

26/2=13 J

30/2=15 J

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29=odd numbers (when the number end in 1, 3, 5, 7, or 9 then it’s odd) J

2, or 4, or 6, or 8, or 10, or 12, or 14>15+ J

It’s confirmed. You can find the answer with this question with this much information.

Step 5:

Conclusion:

You can find the answer with this question with this much information. The options of the answer are 16, 20, 24, and 28. The amounts of each kind of answer is as follows:

28=1 baseball fan and 1 baseball fan were absent.

24=2 baseball fans and 2 baseball fans were absent.

20=3 baseball fans and 3 baseball fans were absent.

16=4 baseball fans and 4 baseball fans were absent.