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Mixed exercises

{{exercise_number}}. Which offer should you choose if you wanted to buy orange juice at the best price? What other criteria may influence your decision?

€3.6

€2.4

€1.8

{{exercise_number}}. The ingredients for coconut bliss balls:

\latex{ 250 } \latex{ g } of crushed biscuits;
\latex{ 50 } \latex{ g } butter;
\latex{ 10} \latex{ g } cocoa;
\latex{ 100 } \latex{ g } powdered sugar;
\latex{ 50 } \latex{ g } coconut shavings;
\latex{ 1 } can of cherry juice.

Tina bought \latex{ 1\;kg } of biscuits, but her brothers ate \latex{ 200 \;g }. Tina wants to use the remaining biscuits to make coconut bliss balls for her birthday party. How much of the other ingredients will she need?

{{exercise_number}}. A cyclist travels \latex{ 1,500 \;m } in \latex{ 5 \;minutes }. How many minutes does it take him to cover a distance of \latex{ 2,400\;m ?}

{{exercise_number}}. The mass of a \latex{ 12\;m } long wire is \latex{ 2.1 \;kg }. What is the mass of a \latex{ 5 \;m } long segment of this wire?

{{exercise_number}}. A group of children from the US is going to a ski camp in Europe, so they are exchanging \latex{ dollars } for \latex{ euros }. Kate bought \latex{ 94 } \latex{ euros } for \latex{ 100 } \latex{ US\,dollars }. How many \latex{ euros } will Neil get for \latex{ 150 } \latex{ US \;dollars? }

{{exercise_number}}. A carpet with an area of \latex{12} \latex{ m^{2} } \latex{( 3 \,m\times4\,m) } costs \latex{ 144\;euros }. How much would \latex{ 15 } \latex{ m^{2} } of the same carpet cost?

{{exercise_number}}. When \latex{ 10 } \latex{ m^{3 }} of ice melts, it results in \latex{ 9 } \latex{ m^{3 }} of liquid water. How much ice is needed to have \latex{ 30 } \latex{ m^{3 }} of liquid water after melting?

{{exercise_number}}. The average fuel consumption of a car is \latex{ 6 } \latex{ litres } \latex{ per } \latex{ 100 } \latex{ kilometres }.

Make a table, and represent the fuel consumption per \latex{ 200 }, \latex{ 300 }, \latex{ 400 }, and \latex{ 500 \,km } in a Cartesian coordinate system.
Use the graph to determine when the car consumed \latex{ 15 }, \latex{ 17, } and \latex{ 20 \;litres } of fuel.
What is the relationship between the fuel consumed and the distance covered?

{{exercise_number}}. A car consumes \latex{ 6 \;litres } of fuel \latex{ per } \latex{ 100 \;kilometres } when travelling at a constant speed on a motorway. If the tank of the car contained \latex{ 40 \;litres } of fuel at the beginning of the journey, how much fuel will be left in the tank after \latex{ 50 }, \latex{ 100 }, \latex{ 150 }, \latex{ 200 }, \latex{ 250 }, and \latex{ 300\; km ?}

Make a table and a graph representing the relationship between the amount of fuel in the tank and the distance travelled.
What is the relationship between the amount of fuel left in the tank and the distance travelled?

{{exercise_number}}. Is there a point in a Cartesian coordinate system that

is part of every graph representing direct proportion?
is not part of any graph representing inverse proportion?

{{exercise_number}}. The entrance fee for a swimming facility is \latex{ 20 \;euros } for adults and \latex{ 15 \;euros } for students.

One day, it turned out that the same number of adults and students entered the facility. How much was the income from the students' entrance fees if adults paid \latex{ 1,200 \;euros ?}
On another day, the income from the two types of fees was equal. How many adult fees were purchased if \latex{ 72 } students entered the facility that day?

{{exercise_number}}. Pete's steps are \latex{ 90\; cm } long, while Kate's steps are \latex{ 80\; cm } long. According to Pete's measurement, one side of the school yard is \latex{ 52 } steps long. How many steps will it take Kate to measure the same distance?

{{exercise_number}}. The circumference of the front wheels of a tractor is \latex{ 120\; cm }, while that of the rear ones is \latex{ 180\; cm }. How many times do the rear wheels turn if the front ones complete \latex{ 126 } turns?

{{exercise_number}}. How many turns does cogwheel A make if cogwheel B turns \latex{ 10 } times? How many turns does cogwheel B make if cogwheel A turns \latex{ 40 } times?

{{exercise_number}}. Angela wants to copy her pictures taken on the ski trip onto a CD for \latex{ 3 } of her classmates. She copied the photos to the first CD at a speed of \latex{ 16x }, which took her \latex{ 2 \;minutes } \latex{ and } \latex{ 36 } \latex{ seconds }. How long will it take her to copy the pictures to the other CDs at a speed of \latex{ 48x? }

{{exercise_number}}. \latex{ 600 \;g } of paint is needed to paint a cube. How many \latex{ grams } of paint are needed to paint a cube with twice as long edges?

{{exercise_number}}. You have \latex{ 5 \;euros } in your left pocket and \latex{ 8 } in your right.

What is the ratio of the money in your left pocket to the money in your right pocket?
The money in your left pocket is how many times the money in your right pocket?
What is the ratio of the money in your left pocket compared to all your money?

{{exercise_number}}. On a hot summer day, \latex{ 160 } scoops of chocolate-flavoured, \latex{ 96 } scoops of vanilla-flavoured, and \latex{ 64 } scoops of strawberry-flavoured ice cream were sold at an ice cream parlour. What is the ratio of the different flavours? Express the ratio in the simplest form.

{{exercise_number}}. The area of a rectangle is \latex{ 24 } \latex{ cm^{2} }. What could the ratio of the adjacent sides be if their lengths in \latex{ centimetres } are whole numbers?

{{exercise_number}}. What is the ratio of the volumes of cubes with \latex{ 1 \;cm } and \latex{ 2 \;cm } long edges?

{{exercise_number}}. What is the ratio of the surface areas of cubes with \latex{ 2 \;cm } and \latex{ 3 \;cm } long edges?

{{exercise_number}}. What is the ratio of the shorter sides of two rectangles with the same area if their longer sides are \latex{ 4 \;cm } and \latex{ 6 \;cm } long?

{{exercise_number}}. The ratio of boys to girls at a school is \latex{ 3:4 }. There are \latex{ 162 } boys. How many students attend the school?

{{exercise_number}}. The ratio of the two sides of a rectangle is \latex{ 4:5 }. One of the sides is \latex{ 26\; cm } long. What is the area of the rectangle?

{{exercise_number}}. Orange syrup should be mixed with water in a ratio of \latex{ 1:7 }. How much orange juice can be made using \latex{ 1.5\; l } of orange syrup? How much water is needed?

{{exercise_number}}. In a survey, children were asked whether they went swimming regularly. The ratio of children who regularly went swimming to those who did not was \latex{ 3:7 }. How many children go swimming regularly if \latex{ 540 } children participated in the survey?

{{exercise_number}}. We shrunk the map on the left. Determine the scale of the shrunken map.

\latex{ 1:10,000 }

Dragon Street

Swan Street

Angel Street

Duck Street

Pilgrim Street

Tallis Street

Hope
Square

Crown Street

Rose Street

Pepper Street

Witch Street

Bride Lane

Witch Street

Pepper Street

Primrose Street

Harp Street

Sun Street

\latex{ 1: }

Milk Street

Knight Street

Cutler Street

Golden Lane

Swan Street

Magpie Street

Moon Street

Arrow Street

Tudor Street

Dragon Street

Swan Street

Duck Street

Tallis Street

Rose Street

Pepper Street

Witch Street

Bride Lane

Sun Street

Pepper Street

Witch Street

Harp Street

Primrose Street

Crown Street

Crane Street

Falcon Street

Hope
Square

Friday Street

Castle Street

Pilgrim Street

Telegraph Street

{{exercise_number}}. At a sports event, basketball, handball and football matches were played. The ratio of basketball, handball and football players was \latex{ 2:3:4. } How many basketball and football players participated in the event if there were \latex{ 48 } handball players?

{{exercise_number}}. One \latex{ kilogram } of Tweety bird seeds costs €\latex{ 4.2 }, while one \latex{ kg } of Chirpy seeds costs €\latex{ 6 }. The two types of seeds are mixed in a \latex{2:3} ratio at a pet store. How much does \latex{ 1\; kg } of the mixture cost?

{{exercise_number}}. The form teacher asked Noe and Kristie to buy fruit syrup for their class's Halloween party. There are \latex{ 30 } students in their class. They will serve the syrup in \latex{ 200 \;ml } cups. Every student should be able to drink at least two cups of juice. How much syrup and water should they buy if the syrup to the water ratio must be \latex{ 1:5 } in each cup?

{{exercise_number}}. The distance between Andrew's and Bob's houses is divided in a ratio of \latex{ 1:2 } by the video store and in a \latex{ 1:1 } ratio by their favourite cinema. How far do Andrew and Bob live from each other if the cinema is \latex{ 150 \;m } from the video store?

{{exercise_number}}. The product of two numbers is \latex{ 150 }, and their ratio is \latex{ 2:3 }. What are the two numbers?

{{exercise_number}}. How many positive, two-digit integers are there whose ratio to a positive three-digit integer is \latex{ 2:3? }

{{exercise_number}}. The ratio of the sum and the difference of two positive numbers is \latex{ 2:3 }. What is the ratio of the two numbers?

Mathematics 6.

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