Sunday, May 08, 2005

Math Problem V

NOTE: The ages in the following word problems are not constant from one question to the next. Mary's age from problem #1, for example, cannot be used to solve for Steve's age in #2.

1) Mary is dating a man, John, who is one and one-half times her age. In John and Mary's jurisdiction, John can be imprisoned for statutory rape if Mary is under the age of 18. If the sum of John and Mary's ages is 50, is John in danger of going to prison if found out?

2) Mary is seeing two men simultaneously, John and Steve. John is one and one-half times Mary's age, and Steve is seven years younger than John. What is the smallest possible value for the sum of their ages if all three are at least eighteen years old?

3) Mary has decided to become a prostitute. Her pimp, Tony Vinylman, requires her to pay him 75 percent of all earnings from her tricks, and she has living expenses of $300 per week. She can perform oral sex twenty-four times per day. How much does she need to charge for oral sex in order to pay her bills, assuming a five-day workweek? How much should she charge if she works every day?

Answers are in comments.

1 comment:

Jessi Guilford said...

1) This is a simple algebra problem. Let Mary's age = x. John's age is then 1.5x. The sum of the ages, 50 is equal to x + 1.5x, or

50 = 2.5x.

Dividing both sides by 2.5, we get:

20 = x.

So Mary's age is 20, and John's age is 30. He is not in danger of going to prison.

2) This is similar to problem 1. Let Mary's age = x. John's age is 1.5x. Steve's age is 1.5x – 7. The sum of their ages is thus

sum = x + 1.5x + 1.5x -7,

which can be simplified to

sum = 4x – 7.

Since John's age will be greater than Mary's regardless of what Mary's is, we only need to evaluate two situations, one where Mary's is 18, and one where Steve's is 18.

Setting Mary's age = 18, we get:

John = (1.5)(18) = 27
Steve = (1.5)(18)-7 = 20.

Setting Steve's age = 18, we get:

18 = (1.5)(x) – 7  11 = 1.5x  x=7 1/3.

Since Mary cannot be seven and a third years old and still be legal, the answer is found by setting Mary's age equal to 18, giving the result

sum = 18 + 27 + 20 = 65.

65 is the answer.

3) Mary can perform oral sex 120 times in a week, and must make $300 from those 120 times. Her share of the earnings is thus ($300 / 120 tricks), or $2.50 per trick.

Since Tony's share of the earnings is 75%, Mary's share is 25%. Thus,

0.25(customer charge) = $2.50

And she must charge $10 per blow job in order to pay her bills.

If Mary works seven days a week, she can perform oral sex (7 x 24) times, which is 168. Figuring this back into the above, her share must be ($300/168), which is $1.79 per trick, and she must charge $7.14 for each.

Obviously, with rates like this, Mary could stand to charge higher rates and accumulate some savings, or develop a crack cocaine habit, or whatever.