Math Problems, Proportions Problems

Problem of the Day: 12/19/12

A rectangular wooden board has a length-to-width ratio of 2:1. If both the length and the width are decreased by 2 inches, the ratio becomes 2.5:1. What is the width of the original board?

Solution to yesterday’s problem:
The problem asks for prime numbers less than 50. Let’s list these prime numbers:

2 3 5 7
11 13 17 19
23 29
31 37
41 43 47

Now we’ll strike through the numbers that don’t satisfy “P+1 divisible by 3” and emphasize the ones that do.

2 3 5 7
11 13 17 19
23 29
31 37
41 43 47

There are 8 prime numbers that satisfy the condition, and 7 that do not – 15 numbers total. So the probability that a number chosen from this group will satisfy the condition is 8/15.

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