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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 25 and the smaller subtracted from the larger equals 9?

smaller number= larger number= Correct Wrong

What two numbers add up to 40 and have a difference of 12?

smaller number= larger number= Correct Wrong

What two numbers add up to 5 and have a difference of 13?

smaller number= larger number= Correct Wrong

There are some rabbits and chickens in a field. Altogether there are 32 heads and 96 legs. How many of each were there?

numbers of rabbits= and chickens= Correct Wrong

The perimeter of a rectangle is 112cm and its length is 16cm 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 227 and the first added to twice the second equals 139.

the first number= second number= Correct Wrong

The difference between the size of the two acute angles of a right-angled triangle is 50o. 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 10 bolts weigh 415g together while 7 nuts and 21 bolts weigh 630g. 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 37 cups of coffee and 36 cups of tea from the studio canteen. They cost him £43.72 altogether. Declan bought 15 cups of coffee and 45 cups of tea and they cost him £38.40 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 126cm and its area is 920cm2. Given that the length is longer than the width find, in centimetres, the dimensions of the rectangle.

rectangle length= width= Correct Wrong


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


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.

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.

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Comment recorded on the 21 October 'Starter of the Day' page by Mr Trainor And His P7 Class(All Girls), Mercy Primary School, Belfast:

"My Primary 7 class in Mercy Primary school, Belfast, look forward to your mental maths starters every morning. The variety of material is interesting and exciting and always engages the teacher and pupils. Keep them coming please."

Comment recorded on the 19 October 'Starter of the Day' page by E Pollard, Huddersfield:

"I used this with my bottom set in year 9. To engage them I used their name and favorite football team (or pop group) instead of the school name. For homework, I asked each student to find a definition for the key words they had been given (once they had fun trying to guess the answer) and they presented their findings to the rest of the class the following day. They felt really special because the key words came from their own personal information."

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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.

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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.


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:

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Description of Levels



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.


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!



Simultaneous Equations Example

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