Savatingiz boʻsh
Mixed exercises
{{exercise_number}}. The image shows the prices of some goods that are sold in the market. Examine them and then answer the following questions.
€\latex{ 2 }/\latex{ kg }
€\latex{ 2.90 }/\latex{ kg }
€\latex{ 3.60 }/\latex{ kg }
€\latex{ 3.10 }/\latex{ kg }
€\latex{ 1.50 }/\latex{ kg }
€\latex{ 1.70 }/\latex{ kg }
€\latex{ 0.40 }/egg
- How much does \latex{ 25 \;kg } of potatoes cost?
- How many \latex{ kg } of apples can you buy for €\latex{ 29 ?}
- If you have €\latex{ 10 } and want to buy ten eggs and \latex{\frac{3}{4}} \latex{ kg } of mushrooms, how much money can you still spend on fruit?
- You want to buy apples, oranges and bananas for a fruit salad. Will €\latex{ 5 } be enough for the fruits if you want to buy at least half a \latex{ kilogram } of each?
Come up with more questions and then answer them.
{{exercise_number}}. The pirates successfully plundered a treasure chest containing \latex{ 8,000 } gold coins. The captain, the helmsman, the first mate, the cook and four seamen took part in the mission. It is the captain's job to decide how the gold will be divided among his crewmembers. For example, the captain takes as much gold as all the others combined, while the helmsman, the first mate, and the cook each receive one-fourth of the amount the captain gets. The remaining coins are then divided equally among the four seamen. Imagine that you are the captain of this pirate crew. Come up with a way to share the treasure and, based on your rules, calculate how many gold coins each crewmember will get.
{{exercise_number}}. Dean added three consecutive integers together. Did he calculate correctly if the sum he got is
- \latex{ 18; }
- \latex{ 25; }
- \latex{ 57 ?}
{{exercise_number}}. Adrian exchanged six €\latex{ 2 } coins for \latex{ 10- } and \latex{ 20- }\latex{ cent } coins of the same total value. How many coins did he get?
{{exercise_number}}. There are \latex{ 25 } \latex{ kilograms } of flour in a bag. In how many different ways can this amount be divided into \latex{ 2-kilogram } and \latex{ 3-kilogram } bags?
{{exercise_number}}. You added \latex{ 1,999 } positive integers together and got an even number as the sum. What can you tell about the product of these numbers?
{{exercise_number}}. Christopher Robin weighed his friends using a two-pan scale. What is the mass of Roo if the scale is balanced
- when Winnie the Pooh is placed in one of the pans, and the other pan contains four bottles of honey of equal mass and a \latex{ 350-gram } weight;
- when Winnie the Pooh and Roo are placed in one of the pans, and the other pan contains four bottles of honey and a \latex{ 500-gram } weight?
{{exercise_number}}. Ash, Ben and Carl counted how many A-s they got last \latex{ year. } Ash and Ben got \latex{ 78 } A-s together, while Ben and Carl got \latex{ 84 } A-s together. The three boys got a total of \latex{ 120 } A-s. How many A-s did Carl get?
{{exercise_number}}. The volume of a pitcher is equal to that of two bottles and two glasses. The volume of five bottles is equal to that of two pitchers and one glass. How many glasses of water can one bottle hold? What about one pitcher?
{{exercise_number}}. A stick is broken into three pieces. The longest piece is four times as long as the shortest, and the middle piece is half as long as the longest. What fraction of the stick is each piece?
{{exercise_number}}. Three envelopes contain money. The second envelope contains three times as much money as the first, and the third envelope contains half as much as the second. If you took €\latex{ 4 } from the second envelope and put it in the third, there would be €\latex{ 9 } more money in the third envelope than in the first one. How much money would be in the third envelope?
{{exercise_number}}. Aunt Julie and Mary are both \latex{ 90 } \latex{ years } old. Aunt Kate is one and a half times as old as when she was one and a half times as old as when she was five \latex{ years } less than half her current age. How old is Aunt Mary?
{{exercise_number}}. Helen picked \latex{ 38 } clovers, either with three or four leaves. She counted their leaves and found that there were \latex{ 120 } in total. How many four-leaf clovers did Helen pick?
{{exercise_number}}. King Dorian divided his \latex{ 18 } castles among his sons. Each son inherited twice as many castles as there were sons. How many sons did King Dorian have?
{{exercise_number}}. There are two more people in front of me in a line than there are behind me. Altogether, there are three times as many people in the line as there are behind me. How many people are in front of me?
{{exercise_number}}. Kenny, Dave, and Mark counted the number of points each of them scored in the town's basketball championship. They found that the three of them scored \latex{ 541 } points together, Dave scored the most, and none of them scored less than \latex{ 150 } points. How many points did Mark score if he and Dave scored \latex{ 346 } points together?
\latex{ }{{exercise_number}}. In the morning, some of the \latex{ 15,324 } bees in a hive flew to the orchard while the rest stayed in the meadow. During the day, \latex{ 1,256 } bees flew from the orchard to the meadow, and \latex{ 2,250 } bees flew from the meadow to a nearby beehive. As a result, there were \latex{ 262 } fewer bees in the orchard than in the meadow. How many bees remained in the orchard?
{{exercise_number}}. Grandpa wonders aloud, 'Time flies. Sixteen \latex{ years } ago, I was three times as old as my son. Now, I am only twice his age.' How old is grandpa?
{{exercise_number}}. A mule and a donkey were carrying a load of sacks. The donkey groaned, so the mule said to him, "Why are you complaining? If you gave me one sack, I would have twice as many as you; and if I gave you one of my sacks, then we would have equal loads."
How many sacks were each of them carrying?
(Euclid)
(Euclid)
{{exercise_number}}. Julie organised one-fourth of the shelves on her bookshelf on Monday. On Tuesday, she organised one-third of the remaining shelves. Then, on Wednesday, she organised half of the rest of the shelves. On Thursday, only two shelves remained to be organised. How many shelves does Julie's bookshelf have? Draw a diagram.
{{exercise_number}}. In the morning, the courier had seven packages to deliver with masses of \latex{ 7; 8; 9; 10; 11; 12 } and \latex{ 13 } \latex{ kilograms }. After delivering the first package, the average mass of the packages became \latex{ 9.5\; kg }. What was the mass of the first package?
{{exercise_number}}. A farmer brought a basket of apples to sell at the market. The first customer bought half of the apples plus half of one more apple. The second customer bought half of the remaining apples plus half of one more apple. The third customer did the same, and so did each customer after that. After the purchase of the sixth customer, who also bought half of the remaining apples plus half of one more apple, the farmer was out of apples. Given that every customer bought only whole apples, how many apples did the farmer bring to the market?
{{exercise_number}}. The built-in navigation system tells the driver which way to turn at each intersection. Where could the car have come from if it followed the following directions?
Left, left, straight, right, left, right, straight, straight, left, right, right, straight.
Centre Bridge
Roosevelt
park
park
King Street
Bread Street
School Street
Fish Street
Milk Street
Milton Street
Broad Street Avenue
Hope
Square
Square
Primrose Street
Grand Boulevard
Peace Street
Rose Street
Little Boulevard
New Street
Square
Square
Wilson Street
Sun Street
Vine Street
Silk Street
Chestnuts
Park
Park
Victory
Square
Square
Cathedral
Square
Square
Temple
Gardens
Gardens
Pilgrim Street
Victoria Avenue
Fort Street
University Street
Student
Park
Park
Friday Street
Flag Street
Hugo Street
