## Golden Ratio

You see here a rectangle with a special shape. The shape has the property that if you make a square at the bottom and cut it off, the remaining rectangle is similar to the original rectangle. That is . Find the ratio of to .

This is a famous ratio, known as the golden ratio. Rectangles of this shape are frequently used in architecture.

## Pickanumba, Give Digits

Ola says to Argyle: Pick your favorite number with no more than three digits. Multiply it by 7, add 2, multiply the result by 13, subtract 25, multiply the result by 11, and subtract 10. Argyle did it. When Ola asked for the 10’s digit, the 100’s digit, and the 1000’s digit of his answer, Argyle replied 7, 3, and 4 respectively. Ola then told him his original number. What was it?

## Sandwiches

Al and Bob are just sitting down to lunch when they are joined by their friend Carol. Al has brought 5 sandwiches to eat, Bob has brought 3, but Carol has not brought any. She does have \$4, however. The three of them divide the food evenly, and then Carol gives Al and Bob her \$4 to pay for her share. How should Al and Bob share the money?

## Eggs to Carry

Your task is to carry 150 eggs from the car to the farm stand. You will be paid two cents for every one that arrives intact; you must pay back five cents for each one that you break. If you want to buy those swim goggles that cost \$2.98 (including tax), how many eggs can you break and still have enough money?

## Restaurant Bill

Sessel ate a lot at his favorite Chinese restaurant, Be Happy in Your Wok, and then he paid his bill. If the bill had been half as much, he would have gotten three times as much change. If the bill had been two dollars more, he would have gotten only half as much change as he actually did get. So how much was his change?

## Golden Oldies

Chris, Ian and Lovejoy found a collection of 72 golden oldies in a flea market. The price for the whole collection was \$9.00. Chris chipped in \$2, Ian \$3, and Lovejoy \$4 to buy them all. If they decided to split up the collection, how many records should each of them keep?

## Farmer Fox Herd of Cows

In his will, Farmer Fox left his herd of cows to his four daughters as follows: The oldest got half of them, the next got 1/4, the third got 1/5, and the youngest got the remaining 7 cows. How many cows were in the herd?

## Comparative Heartbeats Per Year

If you’re in shape, your heart beats about 60 times per minute. If you’re not, it beats faster, say around 80 beats per minute. How many more heartbeats does an out-of-shape heart beat in 1 year than an in-shape heart? (By the way, if you squeeze a tennis ball with your hand, that’s about how hard your heart works when it beats. Squeeze, squeeze, squeeze. . . . Think about it.)