Question

completing a two-way table
a summer camp has 32 campers. 22 of them swim, 20 play softball, and 5 do not play softball or swim. which values correctly complete the table?
○ a=15, b=10, c=7, d=5, e=12
○ a=15, b=7, c=5, d=10, e=12
○ a=14, b=7, c=5, d=12, e=10
○ a=14, b=12, c=7, d=5, e=10
two - way table: rows are swim, do not swim, total; columns are softball, no softball, total. swim row: softball column is a, no softball column is b, total column is 22. do not swim row: softball column is c, no softball column is 5, total column is d. total row: softball column is 20, no softball column is e, total column is 32.

Explanation:

Step1: Find total who don't swim

Total campers = 32, swimmers = 22. So $d = 32 - 22 = 10$.

Step2: Find e (total no softball)

Total no softball: $e = 32 - 20 = 12$? Wait, no. Wait, "do not play softball or swim" is 5 (the "Do Not Swim" and "No Softball" cell). So total no softball: $e = b + 5$. Also, total no swim is $d = c + 5 = 10$ (from step1), so $c = 10 - 5 = 5$.

Step3: Find c

From total softball (20) = a + c, so $a = 20 - c = 20 - 5 = 15$.

Step4: Find b

From total swimmers (22) = a + b, so $b = 22 - 15 = 7$.

Step5: Find e

Total no softball: $e = b + 5 = 7 + 5 = 12$. Also, total no swim is $d = 10$ (from step1). So check the options: a=15, b=7, c=5, d=10, e=12.

Answer:

a = 15, b = 7, c = 5, d = 10, e = 12 (the second option: a=15, b=7, c=5, d=10, e=12)