## Monday, December 6, 2010

### The Solution to Last Week's Puzzle (Word Problem), and a NEW one - Braintenance

Women and Men of Magnificent Mental Magnitude:

Firstly, what is wrong with the following expressions?:

"You can't have your cake and eat it too!"

"Ignorance is bliss..."

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And now, to the solution to last week's dilemma:

Dear Friends:

This is one of those dreaded "word problems" that many of us hated as children in school. The keys to solving any word problem are simple:

1) Read the problem carefully, and find symbols (usually letters) to substitute in for the missing numbers.

2) Create an equation, or several equations which show, mathematically, the relationships between the letters.
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This Mathematical puzzle (#1) is quite easy:

What number, when multiplied by 7 and then increased by 5 will equal 47?

Solution: Create an algebraic equation where x = the unknown number. That equation would look like this: 7X + 5 = 47. If you solve for X, you will find that the mystery number is 6.

This Mathematical puzzle (#2) requires a bit more imagination and creativity:

What two-digit number, when added to itself (but with the digits reversed) and increased by 9 will equal 108?

Solution: You will have to create an algebraic equation, but in this one, understand that the two digit number has one digit in the tens' column and other digit in the ones' column. You might use the variables X and Y, but to express the number, it would be 10X + Y; the number with the digits reversed would be expressed as 10Y + X. The algebraic equation to solve this problem would look like: 10X + Y + 10Y +X +9 = 108. If you simplify and solve the equation you will find out the reduced equation looking like this: X + Y = 9. Weird, eh? Not to worry. Using either simultaneous equations, or trial and error, you'll find that only one combination of X and Y  satisfies both equations (all of the conditions)... one variable must be 5 and the other must be 4.

Accordingly, the original number had to have been either 54 or 45. Two answers? Yep. And either one is correct.

Faithfully,

Douglas Castle

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