## Problem Solving Exercise

25 problems for you to solve starting with the easy ones...

 1 At the beginning of the school year a school library had 3429 books.In Term One they added 134 new books, in Term Two they added 335 books, in Term Three, 291 new books were added and in the final term 139 books were added.How many books did they have in the library at the end of the school year?

2. In the grandstand of a football stadium 78 of the rows of seats are reserved for the home team's fans and the other 122 rows are for the visiting team's supporters. If each row has 110 seats, how many seats are there in the grandstand?

3. A student wants to buy a laptop, a piece of software and a bag. He can choose from three different laptops, three pieces of software and two types of bag. How many different combinations of laptops, software and bags can he choose from?

 4 An airline makes 25 flights per week and each flight carries an average of 231 passengers. If each passenger pays an average of \$168 per flight, how much money did the airline take in total for the year?

5. David left home at 8 a.m. driving at 40 kilometres per hour. His father followed him from home one hour later travelling on the same road at 60 kilometres per hour. At what time did David's father overtake David and how far had they travelled when he did?

6. For a scout camp there are 15 boxes of powdered soft drink. One box of powder makes 32 drinks. If a total of 320 servings are made how many boxes of powder remain?

7. What are the next three numbers and the 15th number in the following sequences?

a. 4, 7, 10, 13, ...
b. 0, 3, 8, 15...

8. The numbers 4 and 9 have three factors. Which is the next number with three factors. Apart from the number of factors, what is the special feature of these three numbers?

Some longer problems:

9. The total number of children in a school is 424. Taking part in the school musical are 31 students from Year Seven, 28 students from Year Eight and 35 from Year Nine. The rest of the school watch the musical from chairs placed in rows. How many rows of chairs will be required if there are 15 chairs in each row?

10. There are 600 members of the FlyHigh flying club. 25% of them are Junior members, 90 of the Juniors are boys. What percentage of the Juniors are girls?

11. John and Jane have \$63 between them. If Jane has five times as much as John, how much does Jane have?

12. The Smith family are going to the movies. The ticket prices are \$10.50 for adults, \$7.50 for children from 10 to 16 and \$3.50 for children under 10. If there are three adults, three children aged 14 and two under-tens, how much change will the family get from a \$100 note?

 13 Bill's Bakery gets a contract to supply a chain of supermarkets with loaves of bread on Sundays. For the first six days of the week it makes 320 loaves per day. If there are 12 supermarkets how many loaves will each supermarket get on a Sunday?

14. Janet saves the stamps of three countries − Canada, Fiji and New Zealand. of her stamps are from New Zealand,  are Fijian and the rest are Canadian. If she has 1000 stamps how many are from Canada?

15. Joanne took 8 minutes to walk from her house to the bus stop, she waited 6 minutes for the bus, and rode the bus for 19 minutes into town. If she left home at 7.50 p.m.,, what time did she arrive in town?

For experts:

16. 80 machines in a factory can produce 4800 identical spoons in 5 hours. At this rate how many spoons would 25 machines produce in 7 hours?

17. A baker bakes a very large cake and Mrs Brown buys half of it. The rest of the cake is divided into 4 equal pieces. Mrs Jones buys one of these pieces and divides it equally between her 3 children. What fraction of the original cake does each of Mrs Jones's children receive?

18. A market gardener estimates that he can supply, on average, a total of 125 carrots from each of 32 rows. For how many weeks can he supply a supermarket needing 10 dozen each day?

19. I thought of a number, doubled it and added three. The result, multiplied by 4 came to 52. What was the original number I thought of?

20. James eats five boxes of chocolates every 30 days. Each packet weighs 420 grams, and each jellybean weighs 5 grams. Find the average rate at which he eats chocolates in "chocolates per day".

 21 A bus leaves its depot with 30 passengers on board. Nine of the passengers get off at the first stop and a third of the remaining passengers ask to be let off at the second stop. What fraction of the original number of passengers remain?

22. A travelling salesman arranges to hire a car to travel from Auckland to New Plymouth and back again. If there is a booking fee of \$30 and an additional cost of 50 cents per kilometre travelled, find the cost of hiring the car if the distance between the two cities is 270 km.

23. At a family gathering, a boy asked his aunt, "What day is your birthday?" The aunt replied " You tell me! The day before yesterday, I was 35 years old and next year I shall be 38." What day is the aunt's birthday?

24. In a one day limited overs cricket match, England batted first against Australia and scored 234 runs in their 50 overs. When a boy turned on the television to watch the final stages of theAustralian innings, exactly 38 overs had been bowled and they needed 6.5 runs each over to win the match. What was the Australian score when the boy started watching?

 25 A reunion was held recently for past pupils of a particular school. One of the former pupils was now a hairdresser and she notes that of those present 3/8 of them had brown hair, 1/4 of them had black hair and a third of them had blonde hair. The nine remaining past pupils had a mix of other colours. How many people were at the reunion?