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Simultaneous Equations

A self marking exercise requiring you to solve a pair of simultaneous equations.

Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Projectable Description Help More

This is level 5; Real life problems that can be solved by writing them as simultaneous equations. You can earn a trophy if you get at least 9 correct. Show all of your working in your exercise book.

What two numbers have a sum of 15 and the smaller subtracted from the larger equals 9?

smaller number= larger number= Correct Wrong

What two numbers add up to 49 and have a difference of 17?

smaller number= larger number= Correct Wrong

What two numbers add up to 5 and have a difference of 11?

smaller number= larger number= Correct Wrong

There are some rabbits and chickens in a field. Altogether there are 58 heads and 194 legs. How many of each were there?

numbers of rabbits= and chickens= Correct Wrong

The perimeter of a rectangle is 124cm and its length is 36cm longer than its width. Find, in centimetres, the dimensions of the rectangle.

rectangle length= width= Correct Wrong

Find two numbers such that twice the first added to three times the second equals 222 and the first added to twice the second equals 140.

the first number= second number= Correct Wrong

The difference between the size of the two acute angles of a right-angled triangle is 6o. Find the size of these two acute angles in degrees.

the smaller angle= larger angle= Correct Wrong

Six years ago a father was twelve times as old as his son. In three years time the father will be three times as old as his son. How old are they now?

the father’s age= son’s age= Correct Wrong

Three years ago a mother was four times as old as her daughter. In nine years time the mother will be twice as old as her daughter. How old are they now?

the daughter’s age= mother’s age= Correct Wrong

11 nuts and 15 bolts weigh 521g together while 5 nuts and 27 bolts weigh 701g. What is the weight of a single nut and a single bolt in grammes?

weight of one nut= one bolt= Correct Wrong

Last month Anthony bought 29 cups of coffee and 32 cups of tea from the studio canteen. They cost him £44.86 altogether. Declan bought 11 cups of coffee and 41 cups of tea and they cost him £41.26 altogether. How much do cups of tea and coffee cost in pence?

one cup of coffee= cup of tea= Correct Wrong

The perimeter of a rectangle is 120cm and its area is 836cm2. Given that the length is longer than the width find, in centimetres, the dimensions of the rectangle.

rectangle length= width= Correct Wrong

Check

This is Simultaneous Equations level 5. You can also try:
Level 1 Level 2 Level 3 Level 4 Level 6

Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

Transum.org

This web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available.

Please contact me if you have any suggestions or questions.

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Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

Comment recorded on the 2 May 'Starter of the Day' page by Angela Lowry, :

"I think these are great! So useful and handy, the children love them.
Could we have some on angles too please?"

Comment recorded on the 3 October 'Starter of the Day' page by Mrs Johnstone, 7Je:

"I think this is a brilliant website as all the students enjoy doing the puzzles and it is a brilliant way to start a lesson."

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Numskull

Numskull

Interactive, randomly-generated, number-based logic puzzle based on the Latin square designed to develop numeracy skills. These puzzles are drag and drop and can earn you a Transum Trophy.

Answers

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Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

Maths Map

Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.

Teachers

If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

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Description of Levels

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Level 1 - Equations that can be added or subtracted to eliminate one variable.

Level 2 - Equations that can be added or subtracted to eliminate one variable after one of the equations has been multiplied by a constant.

Level 3 - Equations that can be added or subtracted to eliminate one variable after both of the equations have been multiplied by constants.

Level 4 - Equations with two variables that are not written in the standard way.

Level 5 - Real life problems that can be solved by writing them as simultaneous equations.

Level 6 - Equations which include fractions in some way.

Extension

There is a printable worksheet to go with this activity. It is an exercise that appeared in an algebra book published in 1895. It starts with basic questions but soon gets tricky!

Worksheet

Example

Simultaneous Equations Example

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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