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home / study / math / advanced math / questions and answers / Dr. Hawk Works In An Allergy Clinic, And His Patients ... Your question has been answered Let us know if you got a helpful answer. Rate this answer Question: Dr. Hawk works in an allergy clinic, and his patie... Bookmark Dr. Hawk works in an allergy clinic, and his patients have the following allergis: 70 are allergic to dairy products, 98 are allergic to pollen, 77 are allergic to animal fur, 13 are allergic to all three, 24 are allergic only to pollen, 10 are allergic only to dairy products, 28 are allergic to dairy products and pollen. What percent of Dr. Hawk's patients are allergic only to animal fur?
Explanation / Answer
70 are allergic to dairy products; 98 are allergictopollen; 77 are allergic to animal fur.
13 are allergic to all three; 24 are allergic to only pollen; 10 are allergic to only dairy products' 28 are allergic to dairy products and pollen;
Total Diary products consists of only dairy + dairy and pollen + dairy and fur + all three
so 70 = 10 + 28+ x + 13 where 'x' is allergic to dairy and fur
x= 70- (51) = 19
Similalry Total Pollen allergic is of only pollen+ dairy and pollen + fur and pollen + all three
98 = 24 + 28+ y + 13
y = 98- 65 = 33
Thus total fur = only fur + fur and pollen + fur and dairy + all 3
77 = a +y+x+13
a (only fur) = 77 - x-y-13 = 64- 19-33 = 64-52 = 12;
Thus total patients allergic to only pollen = 12;
Total number of patients = total dairy + total pollen + total fur - dairy&pollen - dairy&fur - pollen&fur + all 3
T = 70+98+77-28-y-x +13 = 204-19-33 = 204-52 = 152;
Thus percentage of Dr. Hawk's patients allergic to only animal fur = 12/152 * 100 = 7.8947%
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