Question

completing a two-way table
a summer camp has 32 campers. a total of 22 of them swim, 20 play softball, and 5 do not swim or play softball. which values complete the table?
\\(\circ\\) \\(a = 15, b = 10, c = 7, d = 5, e = 12\\)
\\(\circ\\) \\(a = 15, b = 7, c = 5, d = 10, e = 12\\)
\\(\circ\\) \\(a = 15, b = 7, c = 5, d = 10, e = 12\\)
\\(\circ\\) \\(a = 14, b = 7, c = 5, d = 12, e = 10\\)
\\(\circ\\) \\(a = 14, b = 12, c = 7, d = 5, e = 10\\)

	softball	no softball	total
do not swim	\\(c\\)	5	\\(d\\)
total	20	\\(e\\)	32

Explanation:

Step1: Find \( d \) (total do not swim)

Total campers = 32, total swim = 22. So \( d = 32 - 22 = 10 \).

Step2: Find \( c \) (do not swim and play softball)

Do not swim total is \( d = 10 \), and 5 do not swim or play softball. So \( c = 10 - 5 = 5 \).

Step3: Find \( a \) (swim and play softball)

Total play softball = 20, \( c = 5 \). So \( a = 20 - 5 = 15 \).

Step4: Find \( b \) (swim and do not play softball)

Total swim = 22, \( a = 15 \). So \( b = 22 - 15 = 7 \).

Step5: Find \( e \) (total do not play softball)

Total campers = 32, total play softball = 20. So \( e = 32 - 20 = 12 \).

Answer:

\( a = 15, b = 7, c = 5, d = 10, e = 12 \) (corresponding to the option \( a = 15, b = 7, c = 5, d = 10, e = 12 \))