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For The Mathematically Inclined

Contributed by Aadhaarshila
06/19/2003

PROBLEM # 1

In distributing milk at a summer camp it is found that a quart of milk will fill either 3 large glass tumblers or 5 small glass tumblers. how many small glass tumblers can be filled with one large glass tumbler.

PROBLEM # 2

A coffee shop blends 2 kinds of coffee, putting in 2 parts of a 33 cents a pound grade to 1 part of a 24 cents grade. If the mixture is changed to 1 part of the 33 cents grade to 2 parts of less expensive grade, how much will the shop save in blending 100 pounds?

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SOLUTIONS TO PROBLEMS ON 6/05/03

PROBLEM # 1

Three Guernsey cows and two Holstein cows give as much milk in four days as two Guernseys and four Holsteins give in 3 days. Which breed produces more milk? Guernsey or Holstein?

SOLUTION

Assume Guernsey cows produce G gallons in one day and Holstein cows produce H gallons in one day. In 4 days 3G + 2H milk is the same as in 3 days (2G + 4H). Hence,
4(3G + 2H) = 3(2G + 4H)
Simplifying, 6G = 4H
To make both sides equal G has to less than H. So Holstein cows produce more milk.

PROBLEM # 2

Problem - 'Broken calculator' - Every time this calculator is turned on, it shows one of the above characters. But at it seems, the characters come in a pattern, which is described above. Which character is missing? There should be one coming after the 9th character!! It is totally different from the rest of the characters. What is that?

SOLUTION

This calculator is actually displaying the line that it should not and is not displying what it should. So for example number 8 has no lines displayed. If you look carefully , the numbers are in the order 1,2,3,4,5,6,7,8,9 The next number is 0 The displayed line will only be one in the center.



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