## Online Shopper Decision

You are buying a roller on Amazon. Four similar rollers have the same functions, the same price, the same look, but different ratings.

Which product do you choose?

A. 8 positive ratings (8 total ratings)

B. 45 positive ratings (48 total ratings)

C. 90 positive ratings (98 total ratings)

D. 177 positive ratings (198 total ratings)

## JUICE, SODA, and LUCKY

A drinks dispenser has three labelled buttons: JUICE, SODA, and LUCKY. If you press LUCKY you are supposed to get either juice or soda with equal probability.

Each button is wired to exactly one of these functions, but each function is not necessarily wired to exactly one button.

Assuming that you are clever, but unlucky, how many button presses are required to establish exactly which button does which function?

## Markov Chain in Every Day Life

The picture shows a subway map.  A team of inspectors verifies passengers’ tickets at a station on a line, or all lines through it if there are many lines.  Then they randomly choose the next neighboring station and move there to make their inspection.

Subway map

How many times higher is the probability of being inspected at station C than at station A?

Are you eager to know the answer? Try yourself before reading how Markov Chain helps to solve the problem. The answer is here.

The perfect explanation is given in the PBS Infinite Series video:

## Not Knowing Math Can Cost \$15,000

A big number of people can lack basic math skills.

## Car Owner’s Puzzles

Can a specific subject provokes interest to Math?

For example, cars. How much does the gas cost in a month? What speed to choose? When do I need to change the tires? How to be on time? How much do I pay for a car during its life? . . .

What are other intersting subjects? Finance? Love? Sport?

## Consumer Math

#### Leslie Green’s Question

The more debt you get into, the more credit card companies profit. If you buy \$100 of goods at a shop you owe the credit card company \$100, but typically the shop only gets \$98. The shop has to inflate its prices to pay the credit card company. Typically the shop is contractually not allowed to give a discount for cash.  The CostCrashers supermarket chain deals only in cash. The CardPayers supermarkets deal with both cash and credit card transactions, although 75% of people pay by credit card.  All else being equal, how much cheaper could the CostCrashers prices be compared to the CardPayers supermarkets, given the figures stated earlier?

My car uses 10 litres / 100 km and has a 70-litre tank. The Village Garage sells fuel for \$1.40 per litre. It is just several meters from my house. Several garages outside the village sell fuel for \$1.36 per litre. How far could the garage be so that it is worthwhile to drive to and back from the garage to refuel?

#### Income

Bob works 40 years. He does not work on weekends and has a 3-week summer vacation and 7 days of official holidays. The average hourly rate is \$12.5 and he works 8 hours per day.  What is his total income?

#### Stock Price

Every day, a stock price of \$444 is either increased or decreased by 4%. When can it be \$444 again?

#### Inflation

If there is a 500% inflation in a country how much will a 2-dollar telephone cost in one year?

#### Discount

Two successive increases of 25% and 25% are followed by two successive discounts of 25% and 25%.  What percentage is the result?

#### Selling Luxury Cars

If 2 salesmen can sell three luxury cars in 4 days, how many luxury cars can five salesmen sell to six clients in 7 days?

#### Ratio 1 : 2 : 3

Divide \$132 into a ratio 1:2:3. What are the parts?

#### Rebate

Buy 2 for the price of 3 and get 50% off! What is the final rebate do you get?

You find the answers to these and hundreds other Consumer Math’s challenges at http://www.aplusclick.com/money.htm