# Math Puzzle 8

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1) Alley has discovered that a little mouse lives in a hole in the wall of her house. She spreads rat poison around the house hoping to get rid of it. The life expectancy of the mouse varies inversely as the square of the density of poison around the house. When the density of the poison is 1 gm/m

^{2}the life expectancy is 50 days. How long will the mouse survive if the density of the poison is 5 g/m

^{2}?

2) Alley is baking a chocolate almond cake for 8 of her friends who are coming to tea. The recipe is for a cake that will serve 5 people, and calls for 15g of sugar, 250 g of butter, 50 g of chocolate, 75g of almonds and 3 eggs. How much of each ingredient does she have to put so that all her friends will get a full portion?

3) A man must ferry a tiger, a goat, and a head of cabbage across a river. However, his boat is small and he can take only one passenger or object at a time he is also afraid of leaving the three alone because he knows that without supervision, the tiger will eat goat, and the goat will eat the cabbage. How can he bring all three across without losing any of them?

4) Sam has a bet with Alley: he and his friend Thomas can eat 65 pretzels in 5 minutes! Sam can usually eat 6 pretzels in a minute, and Thomas can eat 7. The bet starts, but after three and a half minutes, Sam feels ill and has to stop. How fast must Thomas eat the remaining pretzels in order to win the bet?

5) In a restaurant there was a choice of chicken nuggets, hamburger or salmon with ice –cream, or mousse as a dessert. One third of the diners had chicken nuggets and half of these had ice cream, three eights had hamburger and three fifths of these had ice cream. All those with salmon had mousse, and 470 ice creams were served. How many had salmon?

6) Alley reaches school one morning at 8:23 am. Math class does not start until 8:30 am. But she suddenly realizes that she has left her set squares at home (1056m away). If she can run at a speed of 5.5 m/s, will she be able to run home to get the set-squares and still be on time for roll call?

7) Sam and Alley are trying a new business venture. Every afternoon they set up a lemonade stall at the corner of the street. They make a four and a half liter jug of lemonade using ½ kg sugar (at $16/kg) and 14 lemons

(at $1 per lemon) and sell it in 10 cl(centi liter) paper cups (which cost 40 cent per cup). How much should they sell each cup for if they hope to make a profit of at least 25%?

8) A large publishing house is considering relocating their operations to a country where labour is 18% cheaper. In that same country, however the cost of paper is 13% higher. If the publishing house spends 14million$ on labour and 26million$ on paper every year, would you recommend that they move out or not?

9) The owner of a restaurant needs to buy 30 kg of tomatoes to make soup. The wholesales offers him a discount of 12% on the regular price of tomatoes($8/kg) for such a bulk purchase. Another wholesalers offers the restaurant owner a gift of 3kg tomatoes if he buys the 30 kg at the regular price. Which offer should the restaurant owner accept?(math puzzle 8)

10) Sam goes at to the market to buy a pair of shoes. He is in a dilemma which shop to buy from as each is offering a different successive discount. Can you help him?

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