# A Piggy Bank Bet

My piggy bank has been my trusted repository for some time. I have used it exclusively to save those little extra pennies, nickels, and dimes that I have received as change when I purchase things.

One day I had need of some cash to buy some school supplies before going to classes, so I took “piggy” off my shelf, preparing to make a “withdrawal”. Just then my pesky little sister, Charlene, entered my room and said, “Oh, money! Gimme some, will ya’?”

Being the kind brother that I am, I said, “I’ll make you a deal. If you can guess how much is inside, with less than a 10% error, I’ll give you a quarter. How ’bout that?”

With nothing to lose if she was wrong, “Charlie” shook the bank to hear the clink-clank of the coins, thought a moment, then said, “Ok. I bet there is \$3.50 inside.”

After counting out the money, we found that her guess was pretty good, though not perfect. (But I gave her the quarter anyway; fair is fair, you know.)

I would like for you to tell me how many of each type of coin was in the bank and how much I was left with after paying off my debt to her. You have these facts to work with:

• 14 coins were of one of the three types;
• 16 2/3 % of them were of another type; and
• 3/5 of them were of the third type.

# Shanell’s Holiday Treats

 Shanell’s favorite hobby is baking cakes and cookies to serve her friends and family during holiday occasions. She often buys cashews, pecans, almonds, and walnuts to use in her recipes.

One week, she bought one pound of cashews and two pounds of pecans, and paid \$2.40. The next week she bought four pounds of almonds and one pound of cashews, paying \$3.60. A week later she bought three pounds of walnuts, one pound of cashews and one pound of almonds for \$2.10.

How much would she have to pay on her next trip to the grocery store, if she bought one pound of each of the four types of nuts?

# The King’s Coins

The second half of a famous “Mother Goose” nursery rhyme goes something like this:

 The King was in the counting-house, Counting out his money, The Queen was in the parlour, Eating bread and honey, The maid was in the garden, Hanging out the clothes, When down came a little bird And snapped off her nose!

Now, I have no particular interest in the affairs of those two ladies. As the king’s Royal Mathematician, however, I do have a curiosity about how much money he was counting.

So I went to His Highness to inquire.

His reply to my question as to how many gold coins he had on His counting table was rather unexpected. He said:

“If I put all my coins in stacks of 25 each, I have 15 coins left over in another, shorter stack. If I then put them in stacks of 35 each, I still have 15 left over, just as before. But if I put them in stacks of 45, there are no coins left over. It comes out just right!”

Well, my friends, I’m not called the Royal Mathematician for nothing. I took out my quill, ink bottle and a piece of parchment, and set to work. In no time at all, I knew just how many gold coins the King had.

To answer this problem, tell me the number of stacks of coins the King had in His first counting method.

Remember: define your variables carefully, set up good equations, and use algebraic thinking. (And remember; there were no calculators nor computers in the King’s time!)

BONUS: How does the first half of this famous rhyme go?