An auto insurance company has 10,000 policyholders. Each policy is defined as: young or old male or female; and married or single. Of these policyholders, 3000 are young, 4600 are male, and 7000 are married. The policyholders can also be classified as 1320 young males, 3010 married males, and 1400 young married persons. Finally, 600 of the policyholders are young married males. How many of the company's policyholders are young, female, and single?

Question

Mathematics

Lydon

15 March, 14:17

An auto insurance company has 10,000 policyholders. Each policy is defined as: young or old male or female; and married or single. Of these policyholders, 3000 are young, 4600 are male, and 7000 are married. The policyholders can also be classified as 1320 young males, 3010 married males, and 1400 young married persons. Finally, 600 of the policyholders are young married males. How many of the company's policyholders are young, female, and single?

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Lizbeth Eaton · Answer 1

880

Step-by-step explanation:

This problem a bit annoying, but let's classify the numbers and see where we can get from there:

Total = 10,000

Young = 3,000

Old = 7,000 (not young defined as 10,000 - 3,000)

Male = 4,600

Female = 5,400

Married = 7,000

Single = 3,000

Young Males = 1,320

Young Females = 3,000 (young) - 1,320 = 1,680

Married Males = 3,010

Married Females = 7,000 - 3,010 = 2,990

Young Married = 1,400

Young Married Males = 600

Young Married Females = 1,400 - 600 = 800

Young Female Single = ?

Young Female = 1,680 from above. But not all of them are single.

Young Married Females = 800 from above

Young Female Single = Young Female - Young Married Females = 1,680 - 800 = 880