# Math Solutions and Hints

If you've arrived here, you evidently need math solutions or hints to one of the problems on another page.  That's cool - we are here to help with a math hint that should get you through.  Please quit reading when you think you can figure these out on your own.  Otherwise, I pretty much give away the answer at the end of the hints.

if you want to brush up on your skills, Khan Academy is a free program that really is great. ## Math Game Solutions 1. Eek! Vampires

First of all, we start with 1 and double the number of vampires each night.  So, you could find the answer by doubling until you get to 32, 768 -

1, 2, 4, 8, 16, ...

The relationship is 2^0 or 1, 2^1 or 2, 2^2 or 4 etc..  You would read that as 2 to the 0 power or 1, 2 to the first power or 2, 2 to the second power of 4 etc...  So, one way to phrase the question would be  2^x => 32,768 or what power of 2 is equal to or greater than 34,768.  Another way of stating it would be log base 2 of 32,768.  To find the answer in an excel program, type the following =LOG(32768,2)

## Math Solutions 2 - A dollar left over.

O'k, we start with under \$20 and splitting that amount between two children leaves a dollar.  So, from this tidbit we know that we are dealing with an odd amount of money (if it was even, it would divide evenly) and the amount is less than or equal to \$19.  So, the possible amounts are 1, 3, 5, 7, 9, 11, 13, 15, 17, and 19 dollars.

Now, splitting it between 3 children, still leaves us with \$1 left.  So, we can get rid of all the numbers evenly divisible by 3.  This leaves us with 1, 5, 7, 11, 13, 17, and 19.  If I give each of the three children a dollar, and started with 5, I'd have 2 left over.  What i need is a number that has 1 left over when I divide it by 3.  So that leaves us with 7, 13, and 19.  7 divided by 3 has a remainder of 1, so does 13 and 19.

We are also told that when we divide the money among 4 children, we are left with a dollar.  That is untrue of 7 which has a remainder of 3 and of 19 which also has a remainder of 3.

## #3 - Breaking Even

Warning - Stop reading when you think you've got it figured out.  Otherwise, I will give you the answer.  This is Math Solutions, after all.

The first book sold for \$100 at a 20% loss - So, how much did bob pay for the first book?  Will, he sold the first book for 80% of what he paid for  it (a 20% loss).  So, the formula would be X * .8 = 100.  Divide both sides by .8 and get x = 100/.8 or \$125.  He sold the book for \$100 so he lost \$25 on the first book.

The second book also sold for \$100 but this time it was a 20% gain.  How much did he pay for the second book?  We know that he sold the book for what he paid for it plus 20%.  So, if I multiply the price of the second book times 1 + .2 or 1.2 I should get \$100 (a 20% profit).  My formula becomes x * 1.2 = 100, I divide both sides by 1.2 to get my variable by itself, and get x = 100/1.2 or about \$83.33.  Or a gain of 100 - 83.33 = \$16.67.

Bob lost \$25 but only gained \$16.67 for a net loss of about \$8.33.

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