Algebra In Action
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!
This is level 4: find numbers when given information about the sum or difference of their multiples. You can earn a trophy if you get at least 9 questions correct and you do this activity online.
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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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.
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.
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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
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'.
The sum of two numbers is 25, and the larger is 3 less than three times the smaller. What are the numbers?
Let \(x\) be the smaller number,
then \(3x - 3\) represents the larger number.
$$x + 3x - 3 = 25 \\ 4x - 3 = 25 \\ 4x = 28 \\ x = 7 \\ 3x - 3 = 18$$
The numbers are 7 and 18.
Second Example. Mr Y gave $6 to his three boys. To the second he gave 25 cents more than to the third, and to the first three times as much as to the second. How much did each receive?
Let \(x\) be the number of cents the third boy received,
then \(x + 25\) is the number of cents the second boy received,
and \(3x + 75\) is the number of cents the first boy received.
$$x + x + 25 + 3x + 75 = 600 \\ 5x + 100 = 600 \\ 5x = 500 \\ x = 100 \\ x + 25 = 125 \\ 3x + 75 = 375$$
1st boy received $3.75, 2nd boy received $1.25 and the 3rd boy received $1.00.
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.