Algebra In Action

Transum Software

Real life problems adapted from an old Mathematics textbook (A First Book in Algebra, by Wallace C. Boyden 1895) which can be solved using algebra and common sense!

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This is level 3: find numbers whose sum and difference are given. You can earn a trophy if you get at least 9 questions correct and you do this activity online.

1. In a class of 35 pupils there are 7 more girls than boys. How many girls are there? This Class Has Class	Working:
2. The sum of the ages of two brothers is 43 years, and one of them is 15 years older than the other. How old is the younger brother?	Working: years
3. At an election in which 1079 votes were cast the successful candidate had a majority of 95. How many votes did the successful candidate receive?	Working:
4. Divide the number 70 into two parts, such that one part is 26 less than the other part. What is the larger part?	Working:
5. Lulu and Nusrat together have 143 marbles. If Mrs Brown should give Lulu 15 more, she would have just as many as Nusrat. How many marbles does Nusrat have?	Working:
6. In a storehouse containing 57 barrels there are 3 less barrels of flour than of meal. How many barrels of flour are there?	Working:
7. There were 63 cows in a herd. There were 17 more Jerseys than Holsteins. How many Jersey cows were there?	Working:
8. Two people whose wages differ by 800 dollars receive both together $4400 per month. How much is the higher monthly wage of the two?	Working: £
9. Find two numbers whose sum is 99 and whose difference is 19. Multiply the two numbers together.	Working:
10. Divide 62 into three parts such that the first part is 4 more than the second and the third 7 more than the second. What is the second number?	Working:
11. Three people together received £34200; if the second received £1500 more than the first, and the third £1200 more than the second, how much did the first person receive?	Working:
12. A farmer owns three farms. In the first there are 5 acres more than in the second and 7 acres less than in the third. If there are 53 acres in all the farms together, how many acres are there in the third farm?	Working: acres

This is Algebra In Action level 3. You can also try:
Level 1 Level 2 Level 4 Level 5 Level 6 Level 7

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.

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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:	Alternatively, if you use Google Classroom, all you have to do is click on the green icon below in order to add this activity to one of your classes.	It may be worth remembering that if Transum.org should go offline for whatever reason, there is a mirror site at Transum.info that contains most of the resources that are available here on Transum.org. When planning to use technology in your lesson always have a plan B!
Transum, Sunday, January 26, 2014 "These questions have been adapted from 'A First Book in Algebra' by Wallace Boyden. They all are designed to encourage an algebraic solution by setting up an equation (or alternatively simultaneous equations) and solving it. Some of the questions could be classified under the topic of ratio. In his introduction Wallace Boyden states 'Algebra is so much like arithmetic that all that you know about addition, subtraction, multiplication, and division, the signs that you have been using and the ways of working out problems, will be very useful to you in this study. There are two things the introduction of which really makes all the difference between arithmetic and algebra. One of these is the use of letters to represent numbers, and you will see in the following exercises that this change makes the solution of problems much easier.'." I'm Not A Humanist But..., Planet Earth Saturday, May 24, 2014 "On level 4 of the 'algebra in action' section, question 11 says: "Divide the number 137 into three parts, such that the second is 3 more than the first, and the third five times the second. What is the third part?" The answer is 100, but it was marked as being wrong, so I tried again, but with 20 (the second number) and 17 (the first number) and it marked 17 as being correct. Just thought you should know about this mistake so that you can correct it. [Transum: Thank you so much for taking the time to highlight this error. You were indeed right and the error has now been corrected. Thank you so much.]" Nick Staples, Waipahu Intermediate Wednesday, August 18, 2021 "Is there a way these algebra in action activities can be made into printable worksheets please. [Transum: Thanks for your feedback Nick. Most of the Transum online exercises can be printed directly from your browser. The input boxes transform into dotted lines for pupils to write their answers on and if the page is being printed by a Transum subscriber, the answers appear at the bottom of the worksheet.]"

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Description of Levels

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Level 1 - Find two values given their ratio and either their sum or difference

Level 2 - Find one of three numbers given the connection between them

Level 3 - Find numbers whose sum and difference are given

Level 4 - Find numbers when given information about the sum or difference of their multiples

Level 5 - More questions similar to those in previous levels

Level 6 - Yet more questions similar to those in previous levels

Level 7 - The algebra involved in this level includes fractions

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.

Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

Back in 1895 Mr Boyden wrote 'Algebra is so much like arithmetic that all that you know about addition, subtraction, multiplication, and division, the signs that you have been using and the ways of working out problems, will be very useful to you in this study. There are two things the introduction of which really makes all the difference between arithmetic and algebra. One of these is the use of letters to represent numbers, and you will see in the following exercises that this change makes the solution of problems much easier'.

Example for level 3

Divide the number 126 into two parts such that one part is 8 more than the other.

Let \(x\) represent the smaller part,
the larger part is then \(x + 8\)
$$x + x + 8 = 126 \\ 2x + 8 = 126 \\2x = 118 \\ x = 59 \\ x + 8 = 67$$
The parts are 59 and 67.

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. You can double-click the 'Check' button to make it float at the bottom of your screen.

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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