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Think of a Number

Ten students think of a number then perform various operations on that number. You have to find what the original numbers were.

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This is level 4: THOAN problems with the result a multiple of the number. You can earn a trophy if you get at least 7 questions correct.

Thinking HeadsLuis once said:
'I think of a number. I multiply it by 3, add 9, divide by 2, and then subtract 6. The result is the same number that I started with.'
What number was Luis first thinking of?

Working:

Correct Wrong


Owen says:
'I think of a number. I multiply it by 4, subtract 16, divide by 2, and then add 6. The result is the same number that I started with.'
What number was Owen first thinking of?

Working:

Correct Wrong
Landon says:
'I think of a number. I add 5, multiply the result by 2, subtract 6, and then divide by 2. The result is twice the number that I started with.'
What number was Landon first thinking of?

Working:

Correct Wrong
Diego says:
'I think of a number. I triple it, add 9, divide by 3, and then subtract 4. The result is half the number that I started with.'
What number was Diego first thinking of?

Working:

Correct Wrong
Brian says:
'I think of a number. I multiply it by 2, add 6, divide by 3, and then subtract 1. The result is half the number that I started with.'
What number was Brian first thinking of?

Working:

Correct Wrong
Adam says:
'I think of a number. I subtract 2, multiply the result by 4, add 8, and then divide by 2. The result is three times the number that I started with.'
What number was Adam first thinking of?

Working:

Correct Wrong
Adrian says:
'I think of a number. I add 3, multiply by 2, subtract 4, and then divide by 5. The result is twice the number that I started with.'
What number was Adrian first thinking of?

Working:

Correct Wrong
Kyle says:
'I think of a number. I multiply it by 4, add 8, divide by 3, and then subtract 6. The result is the same number that I started with.'
What number was Kyle first thinking of?

Working:

Correct Wrong
Eric says:
'I think of a number and subtract it from 22. The result I divide by double the number. Finally I add 5 and find the result is 10.'
What number was Eric first thinking of?

Working:

Correct Wrong
Ian says:
'I think of a number. I subtract three lots of that number from 100 then I add two and a half. The result I get is double my original number plus 50.'
What number was Ian first thinking of?

Working:

Correct Wrong
Check

This is Think of a Number level 4. You can also try:
Level 1 Level 2 Level 3

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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Description of Levels

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Level 1 - Whole number THOAN problems

Level 2 - Decimal THOAN problems

Level 3 - Negative decimal THOAN problems

Level 4 - THOAN problems with the result a multiple of the number

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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Curriculum Reference

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

Example

Daniel says 'If I double my number and add 6 the answer is 30'

Method 1 - Work backwards

Start at the end of the sentence with the answer 30 and undo all of the operations Daniel performed on his number in reverse order.

30 minus 6 then divide by two

The number Daniel was thinking about was 12

 

Method 2 - Form and solve an equation

Let the number that Daniel is first thinking of be n.

2n + 6 = 30

Subtract 6 from both sides

2n = 24

Divide both sides by 2

n = 12

The number Daniel was thinking about was 12

 

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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