Missing Price

When I went to the store, I purchased four items. The following shows the cost of three of the items:

 $1.50
 $3.00
 $4.00

The line to the checkout was pretty long, so to quench my boredom I started playing with my pocket calculator while waiting.

I found out, to my surprise, that the four prices of the four items I purchased added to the same number as I got when I multiplied the four prices together.

What was the price of the fourth item?

Answer:

The three prices add to 1.50 + 3.00 + 4.00 = $8.50.
The three prices multiply to 1.50 x 3.00 x 4.00 = $18.00.
You might be able to see that adding another $0.50 will take the total to $9.00, and multiplying by another $0.50 will take the product to $9.00 also, but the answer can also be found using algebra. Let's call the unknown price P:

 1.50 + 3.00 + 4.00 + P = 1.50 x 3.00 x 4.00 x P
 8.50 + P = 18.00 x P
 8.50 = 18.00 x P - P
 8.50 = 17.00 x P
 8.50/17.00 = P
 P = 0.50.
 

Area of a Square!

You have a piece of paper, 10cm by 10cm. Area = 100cm^2. For some reason, you need a square piece of paper with an area of 50cm^2. Using the paper you have, what's an easy way of getting the new square?

 

Answer:

Fold the four corners of the square into the centre. This doubles the thickness of the paper, and so halves the area.

Monk Steps

A monk has a very specific ritual for climbing up the steps to the temple. First he climbs up to the middle step and meditates for 1 minute. Then he climbs up 8 steps and faces east until he hears a bird singing. Then he walks down 12 steps and picks up a pebble. He takes one step up and tosses the pebble over his left shoulder. Now, he walks up the remaining steps three at a time which only takes him 9 paces. How many steps are there?

 

Answer:

There are 49 steps.

He climbs halfway, which is step 25. He hears the bird singing on step 33. He picks up the pebble on the 21st step and tosses it on the 22nd step. The remaining 27 steps are taken three at a time which is 9 paces.


 

How Many Campers?

Camp Pineveiw's cook, Margaret Johnson, was just about to begin preparing the picnic lunch for all the campers. She already knew she needed to fill 55 bowls of the same size and capacity with the same amount of food. When she was done, she decided to read the guidelines for the picnic, just out of curiosity. The guidelines said:

 1. Every camper gets their own bowl of soup.
 2. Every two campers will get one bowl of spaghetti to share.
 3. Every three campers will get one bowl of salad to share.
 4. All campers are required to have their own helping of salad, spaghetti, and soup.

After some rapid calculations, Margaret was able to figure out how many campers were going to the picnic. Can you?

 

Answer:

30 campers.

Troubling Doubling at School

Read the little poem and answer its question if you can.

 The number of girls who do wear a watch
 is double the number who don't.
 But the number of boys who do not wear a watch
 is double the number who do.
 If I tell you the number of girls in my class
 is double the number of boys,
 Can you tell me the number I teach? Here's a clue:
 More than 20; below 32!

 

Answer:

27

Solution:

The number of boys must be a multiple of 3 (3, 6, 9...) so that it can be split in the ratio of 2:1 (no watch:watch).
The number of girls is double the no. of boys (6, 12, 18...)
So the totals can only be 9, 18, 27...