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Mathematics 6.

Table of contents
Look at the information
Trip to Paris
Offers for Individual Travelers
Our travel agency thought of those who would like to take part in well planned programs in addition to their individual program. Discover the cultural capitals of the world with the help of our well trained guides.
Join the 
programs of our groups
in Paris!
\latex{\textcolor{ee255a} \blacksquare} Paris city tour by bus + Boat trip on the Seine river + visit to the Eiffel tower • €\latex{40 }/per + ticket to the Eiffel tower (\latex{ 1.–2.–3. } levels \latex{ 4.20–7.70–11 } euros • From \latex{ 2 } pm to the evening.
\latex{\textcolor{90539d} \blacksquare} Trip to Versailles +Walk in Paris • €\latex{38 }/per • Versailles, Arc de Triomphe, Champs-Élysées, Musée d’Orsay • From \latex{ 9 } am to the evening. Museum pass (\latex{ €30 }) required.
\latex{\textcolor{fdc33d} \blacksquare} Two day Paris city tour • €\latex{45 }/per • Louvre (English guided tour), Montmartre, Sacré Coeur, Place du Tertre, Ile de la Cité, Notre Dame, Seine shore, Latin district.
\latex{\textcolor{00a457} \blacksquare} Eurodisney • €\latex{20 }/per + ticket to Disney Park (adult \latex{ 43 } euros, child \latex{ 35 } euros) • From \latex{ 9 } am to \latex{ 9 } pm.
\latex{\textcolor{16acea} \blacksquare} Walk in Paris + Louvre with English guided tour • €\latex{35 }/per • Louvre, Les Invalides, Napoleon’s tomb, walk in the Opera district, and introduction to perfume produc tion in the Fragonard perfum museum. The program starts at \latex{ 9 } and lasts until the evening. Museum pass required.
DISCOUNTS!

Specials for taking part in several programs:
\latex{ 2 } day: \latex{ 2 } from both programs;

\latex{ 3 } day: \latex{ 3 } from all three programs;

\latex{ 4 } day: \latex{ 4 } from all four programs.
The dates of the programs
\latex{ 2006 }
\latex{ 1 }
\latex{ 2 }
\latex{ 3 }
\latex{ 4 }
\latex{ 5 }
\latex{ 6 }
\latex{ 7 }
\latex{ 8 }
\latex{ 9 }
\latex{ 10 }
\latex{ 11 }
\latex{ 12 }
\latex{ 13 }
\latex{ 14 }
\latex{ 15 }
\latex{ 16 }
\latex{ 17 }
\latex{ 18 }
\latex{ 19 }
\latex{ 20 }
\latex{ 21 }
\latex{ 22 }
\latex{ 23 }
\latex{ 24 }
\latex{ 25 }
\latex{ 26 }
\latex{ 27 }
\latex{ 28 }
\latex{ 29 }
\latex{ 30 }
\latex{ 31 }
March
April
May
BUS TICKETS
Main season
Pre(post)season
Bp.–Paris–Bp.
\latex{ VI.1.–VIII. 20. }
\latex{ VIII. 20.–VI.1. }
full fare
infant
child
youth
above
\latex{ 60 }
advance purchase
(\latex{ 0–4 }years)
(\latex{ 4–12 } years)
(\latex{ 12–26 } years)
(min. \latex{ 30 } days)
€\latex{ 120 }
€\latex{ 110 }
€\latex{ 24 }
€\latex{ 23 }
€\latex{ 60 }
€\latex{ 58 }
€\latex{ 96 }
€\latex{ 93 }
€\latex{ 96 }
€\latex{ 93 }
€\latex{ 72 }
€\latex{ 70 }
Before solving an exercise, collect all the information that is needed to answer the question(s). Usually, most of the relevant, and sometimes irrelevant, information is provided in the text. However, in the case of practical exercises, you may have to search for additional information in order to solve the problem.

 

Find newspaper articles containing numbers. Come up with questions that you can answer based on the articles.

Example 1
Reka is \latex{ 25 }, her brother Andy is \latex{ 11 } years old. They would like to travel to Paris from Budapest on the \latex{ 21 }st of April for two weeks. They got the pamphlet above at the travel agency.
How much does the bus cost for both of them, if
  1. they can buy their tickets at least \latex{ 30 } days before the trip;
  2. they can only buy their tickets \latex{ 1 } week before the trip?
Solution
We have to find the information in the table about the bus ticket prices that are relevant to Reka’s ticket.
April \latex{ 21 }st is in the pre-season, so we have to look at the second row. Naturally we would like to buy the least expensive ticket that we can (only one discount can be used at one time).
  1. In Reka’s case, the advance purchase ticket is the cheapest €\latex{ 80 }. In case of her brother, the child ticket is the cheapest €\latex{ 65 }. Altogether: \latex{80+65=145}€.
The return trip for the two of them costs €\latex{ 145 }.
  1. If they cannot purchase tickets in advance, Reka should buy the youth ticket, it costs €\latex{ 120 }. The least expensive ticket for the brother now is €\latex{ 65 }. 
Altogether: \latex{120+65= 185} €.
The return trip for the two of them costs €\latex{ 185 }.
Exercises
{{exercise_number}}. In addition to their own programs, Reka and her brother would like to take part in some of the travel agency’s programs as well. Help them plan a program and calculate the costs based on the travel agency’s offers for
  1. two days;
  1. three days;
  1. four days.
{{exercise_number}}. Gabe is \latex{ 11 } years old and \latex{ 156 \,cm } tall, weighing \latex{ 42 \,kg }. His friend Ben weights \latex{ 45 \,kg } and is \latex{ 158 \,cm } tall. Who is taller, and by how much?
  • Write down the information needed to answer the questions.
  • Write down the information that is not necessary for answering the questions.
{{exercise_number}}. The area of Hungary is \latex{ 93,030 } \latex{km^{2}}, it has about \latex{ 10,000,000 } inhabitants. Canada has about \latex{ 22,800,000 } inhabitants, its area is \latex{ 9,975,030 } \latex{km^{2}} (\latex{755,169\,km^{2}} of this is water). The area of which country is larger, and by how much?
  • Write down the information needed to answer the questions.
  • Write down the information that is not necessary for answering the questions.
{{exercise_number}}.The largest land mammal is the male African elephant, it is \latex{ 3.7 \,m } tall and weights \latex{ 7 \,t }. The smallest mammal is the Proboscis bat, it weights \latex{ 2 \,g } and is \latex{ 33 \,mm } long. (We considered the average size of adult individuals.)
How many times more does the African elephant weight, than the Proboscis bat?
  • Write down the information needed to answer the questions.
  • Write down the information that is not necessary for answering the questions.
{{exercise_number}}. 
Garden Gnome reserve in England
The world’s largest garden gnome collection
is located in Little Town,England.
Anne Atkin has been collecting gnomes since \latex{ 1978 }.
She created a \latex{ 1.61 } hectare gnome reserve in \latex{ 1988 },
and populated it with \latex{ 2010 } gnomes.
Her interesting collectionhas drawn over
\latex{ 105,000 } visitors over \latex{ 18 } years.
  1. How many years did it take Atkin to collect the record breaking number of gnomes?
  2. How many square metres are the gnomes arranged on?
  • Write down the information needed to answer each question.
  • Is there any required information that is not in the text?
  • Write down the information that is not necessary for answering the questions.
{{exercise_number}}. The Oxford–Cambridge boat race is held on the River Thames each year. The distance is \latex{ 6,748 \,m } long. There are \latex{ 8 } rowers and a coxswain. On average they row \latex{ 35 } times a minute. One race lasts about \latex{ 18 } minutes.
  1. How many rows does it take to complete the race?
  2. How many metres do they travel per minute?
  • Write down the information needed to answer each question.
  • Is there any required information that is not in the text?
  • Write down the information that is not necessary for answering the questions.
{{exercise_number}}. The graph shows normal bodyweight for children. In case of normal body weight the values of height and weight fall in the coloured part. How much could a \latex{ 145 \,cm } tall child weigh, if he/she falls in the normal range? Think of further questions that can be answered based on the graph, then answer them.
height (cm)
weight (kg)
\latex{ 190 }
\latex{ 180 }
\latex{ 170 }
\latex{ 160 }
\latex{ 150 }
\latex{ 140 }
\latex{ 130 }
\latex{ 120 }
\latex{ 110 }
\latex{ 100 }
\latex{ 90 }
\latex{ 80 }
\latex{ 10 }
\latex{ 20 }
\latex{ 30 }
\latex{ 40 }
\latex{ 50 }
\latex{ 60 }
\latex{ 70 }
\latex{ 80 }
\latex{ 90 }
\latex{ 100 }
{{exercise_number}}. Colonel Ernest Loftus from Zimbabwe started a diary on May \latex{ 4 }th \latex{ 1896 } at the age of \latex{ 12 } and continued it to his death on July \latex{ 7 }th, \latex{ 1987 }.
  1. How old was the Colonel when he died?
  2. How many years did he write his diary for?
  • Write down the information needed to answer each question.
  • Is there any required information that is not in the text?
  • Write down the information that is not necessary for answering the questions.
{{exercise_number}}. A Santa bought \latex{ 200 } of the same gift packs. How much did he have to pay for all the packs? What information do we need to solve the exercise?
{{exercise_number}}. There are four children in a family. The oldes is \latex{ 8 }, the youngest is \latex{ 2 } years old. The sum of their ages is \latex{ 20 } years now. What will the sum of their ages be in \latex{ 3 } years?
{{exercise_number}}. Let \latex{ A, B, C, D } and \latex{ E } be different digits. Look for \latex{ B+D } if we know the relations shown in the figure. 
\latex{ A }
\latex{ B }
\latex{ + }
\latex{ C }
\latex{ C }
\latex{ D }
\latex{ + }
\latex{ E }
\latex{ A }
{{exercise_number}}. The diagram shows the water consumption of one person on each continent. The table shows the division of water use in European households. Analyze the data. Ask question and answer them.
litre
\latex{ 200 }
\latex{ 100 }
\latex{ 0 }
\latex{ 146 }
\latex{ 212 }
\latex{ 54 }
\latex{ 28 }
\latex{ 59 }
Europe
N. America
S. America
Africa
Asia
distribution of daily water consumption per capita in a European household
washing
drinking,
cooking
dishwashing
bath
body care
cleaning
toilet
garden
car wash
\latex{ 20 } litres
\latex{ 5 } litres
\latex{ 12 } litres
\latex{ 40 } litres
\latex{ 10 } litres
\latex{ 6 } litres
\latex{ 45 } litres
\latex{ 5 } litres
\latex{ 3 } litres
Quiz
If we blow out four of five burning candles, how many candles are left?