Zachary thinks of a number.
He then does the following operations:
Multiply by 3, subtract 3, multiply by 2 then add 36 (in that order).
He finds that the number he ends up with is 12 times his original number.
What was Zachary's original number?
How did you use this starter? Can you suggest
how teachers could present or develop this resource? Do you have any comments? It is always useful to receive
feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.
Click here to enter your comments.
If you don't have the time to provide feedback we'd really appreciate it if you could give this page a score! We are constantly improving and adding to these starters so it would be really helpful to know which ones are most useful. Simply click on a button below:
This starter has scored a mean of 2.1 out of 5 based on 191 votes.
This question is best answered by forming an algebraic equation then solving it. Let Zachary's original number be x.
First operation gives 3x
Second operation gives 3x- 3
Third operation gives 2(3x- 3)
Fourth operation gives 2(3x- 3) + 36
This is equal to 12 times the original number
2(3x - 3) + 36 = 12x
6x- 6 + 36 = 12x
x = 5
Zachary's original number was 5.
Note to teacher: Doing this activity once with a class helps students develop strategies. It is only when they do this activity a second time that they will have the opportunity to practise those strategies. That is when the learning is consolidated. Click the button above to regenerate another version of this starter from random numbers.
Teacher, do your students have
access to computers?
Here is the URL for a concise version of this page without comments or answers.
Here is the URL which will take students to our eQuation Generator which provides unlimited practice solving linear equations.