CAPÍTULO II MARCO TEÓRICO
2.9 La logística empresarial y su estructura
2 Divide $70 in the ratio of 4 : 3
10 If the price of unleaded petrol was $1.70 per litre, what would it cost to fill a 50 L tank?
Mental Computation
You need to be a good mental athlete because many everyday problems are solved mentally
Why is 0.4047 hectares like a bad tooth?
Because it is an acre.
If you’re not lighting any candles, don’t complain about being in the dark.
Exercise 11.12
1 William worked for 6 hours and was paid $22 per hour. How much did William earn?
2 Isabella bought a box of 100 stamps for $65. What is the cost of 1 stamp?
3 The ratio of cattle to sheep is 1 : 4. If there are 20 sheep, how many cattle?
4 There is 45 kg of mortar. The ratio of cement to sand in the mortar mix is 1 to 4. How many kg of cement is in the mortar?
5 Cooper needs to travel by bus for 21 days in June. A daily ticket will cost him
$5.80 and a monthly ticket will cost him $109.20. What is his average daily saving if Cooper buys a monthly ticket?
6 A bike priced at $220 was discounted by 20%.
What is the discounted price?
7 In 2010 there were 120 Year 12 Students.
48 of them were offered a place at a University.
What percentage of students weren’t offered a University place?
8 What percentage of the marbles are white?
9 Change 323 to a vulgar fraction.
10 Change 1115 to a mixed fraction.
11 A cake has 3 blue candles and 9 white candles. What fraction of the candles are blue?
12 A shortcut for adding GST (10%) is to multiply by 1.1. What would be the shortcut for adding 20%? Use the shortcut to increase $4 by 20%
13 On Wednesday Chloe completed 70% of the project. On Thursday she
completed 50% of the remainder of the project. What percentage of the whole project did she complete on Thursday (Assume 100 at the start of the project)?
14 The paddock grew 800 pumpkins. One-quarter of them were unsuitable for market. 20% of the marketable pumpkins were exported. How many pumpkins were exported?
15 If 1 Australian dollar buys 0.90 US dollars, how many US dollars could be bought with 20 Australian dollars using this exchange rate?
16 The car uses 5 L of petrol per 100 km. How far would the car travel on $30 of petrol at $1.50 per litre?
17 The distance from A to B is four times the distance from B to C. The distance
Mixed fraction Vulgar fraction
223 83
Competition Questions
Exercise 11.13
On a farm with 50 horses and 70 cattle, 30% of the horses are lame and 10% of the cattle are lame. What percentage of the animals are lame?
Lame horses = 0.3 x 50 Lame cattle = 0.1 x 70
= 15 = 7
% lame = (15 7(50 70++)x100) % lame = 18.33
1 On a farm with 10 horses and 40 cattle, 10% of the horses are lame and 20% of the cattle are lame. What percentage of the animals are lame?
2 The junior orchestra consists of 20 Year 9 students and 30 Year 8 students. If 15% of the Year 9s play the trumpet and 20% of the Year 8s play the trumpet, what percentage of the orchestra play the trumpet?
When GST (10%) is added to an item, the price is $66. What was the price of the item before GST was added? Let p be initial price.
66 = p + 0.1p
66 = p(1 + 0.1)
66 = p × 1.1
66 ÷ 1.1 = p $60 = Price before GST
When an item is discounted by 15%, the price is $34. What was the price of the item before it was discounted?
34 = p − 0.1p
34 = p(1 − 0.1)
34 = p × 0.85
34 ÷ 0.85 = p
$40 = Price before discount
3 When GST (10%) is added to an item, the price is $88. What was the price of the item before GST was added?
4 When GST (10%) is added to an item, the price is $77. What was the price of the item before GST was added?
5 When an item is discounted by 15%, the price is $68. What was the price of the item before it was discounted?
6 When an item is discounted by 25%, the price is $45. What was the price of the item before it was discounted?
7 Simplify the ratio 24 : 36 : 15 : 27
8 A, B, C, D share $500 in the ratio 1 : 2 : 3 : 4. How much does B get?
9 A, B, C, D share in the ratio 1 : 2 : 3 : 4. If B gets $500, what was the original total?
10 Neba bought some cushions. If GST (10%) hadn’t been added to the cost, Neba would have been able to buy an extra cushion. How many cushions did Neba buy?
A shortcut for finding the price before GST was added:
divide by 1.1 Why?
Build maths muscle and prepare for mathematics competitions at the same time.
Investigations
Investigation 11.1 Gear Ratios
Bring a bike into the classroom, and when in lowest gear, turn it upside down.
1 Turn the pedals through 10 revolutions.
2 Count the number of times the rear wheel turns.
3 Determine the gear ratio (the ratio of pedal turns to rear wheel turns).
4 Repeat for the top gear.
Why use gears?
Why the difference in gear ratios between the lowest gear and the highest gear?
Can you name 10 other machines that use gears?
Can you find the gear ratio by counting the teeth?
Investigation 11.2 Population Comparison
Use the Internet to investigate Australia’s population change:
• current population.
• current birth rate.
• current death rate.
• current immigration rate.
Can you predict Australia’s population in ten years time?
Compare this with an investigation of Indonesia’s population change.
Compare this with an investigation of other Asian countries.
Investigation 11.3 Real Life
Applications of percentages and rates are everywhere.
1 Can you make a list of 20 applications of percentages?
2 Can you make a list of 20 applications of rates?
Investigation 11.4 Triangular Numbers
The numbers 1, 3, 6, 10, …. are Triangular numbers because they form triangles.
1 What are the next four Triangular numbers?
2 What do you notice about the sum of any two consecutive Triangular numbers?
1 3 6
Astronomers
study the movement, origins, and properties of the stars, planets, and galaxies.• Relevant school subjects are Mathematics and Physics.
• Courses range from Universtity Bachelor degrees to Master degrees.
Exercise 11.14
1 The digits of 122 are 1, 2, and 2, and 1 + 2 + 2 = 5. Find ten other numbers whose digits add to give 5.
2 Write 15 as the sum of three consecutive numbers.
3 Write 15 as the sum of five consecutive numbers.
4 How many great-great-great-grandparents did you have?
5 How long would it take to count to one million if you counted once every second?
6 Score a century. Use +, –, x, ÷, and brackets between the numbers 1 2 3 4 5 6 7 8 9 to make exactly100.
7 Blocko is building a set of steps out of blocks and the first 3 steps are shown.
How many blocks will be needed to build 10 steps?
Elevens Make eleven marks on a piece of paper.
Each of two players take turns to mark off one or two of the marks.
The loser is the person who crosses off the last mark.
▌ ▌ ▌ ▌ ▌ ▌ ▌ ▌ ▌ ▌ ▌
1 Put 20 objects in a container (eg. centicubes, coins).
2 Turn your back and ask someone to take from
1 to 9 objects and put them in their pocket. They take 6 3 Ask them to count the number left. 14 are left 4 Ask them to total the digits of the number left. 1 + 4 = 5 5 Ask them to take that many from the container
and to add them to their pocket. They take 5 6 Ask them to take as many as they like from those
left in the container and to keep these in their hand. They take 3 7 You tell them how many they have in their hand.
A Couple of Puzzles
A Game
A Sweet Trick
Count the number left in the container, ie 6, and subtract from 9.
9 - 6 = 3. They have 3 in their hand.
Practice the trick a couple of times before you use it.