No Matter
After performing some operations, what number is your answer always a multiple of?
Age
11 to 14
Challenge level
Problem
Think of a whole number, double it, then add 3.
Multiply your answer by 4 and then take away 5.
Now take away the number you first thought of.
Your answer will always be a multiple of which number?
Student Solutions
Answer: a multiple of $7$.
Using letters
Let the number thought of be $x$
Double it, then add 3: $2x+3$
Multiply your answer by 4: $4(2x+3)=8x+12$
And then take away 5: $(8x+12)-5=8x+7$
Now take away the number you first thought of: $(8x+7)-x=7x+7 = 7(x+1)$ multiple of $7$.
Using a diagram
Think of a whole number
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double it, then add 3
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Multiply your answer by 4 and then take away 5
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Now take away the number you first thought of
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Your answer will always be a multiple of which number?
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