Itchy's fleas
Itchy the dog has a million fleas. How many fleas might his shampoo kill?
Age
14 to 16
Challenge level
Problem
Itchy the dog has a million fleas.
His anti-flea shampoo claims to leave at most $1\%$ of the original number of fleas.
What is the minimum number of fleas that the shampoo will remove?
Student Solutions
Answer: $990\ 000$
$1\%$ is the same as $\frac{1}{100}$, and $1\ 000\ 000 \div 100 = 10\ 000$.
Therefore, at most $10\ 000$ fleas will remain after the treatment.
This means at least $1\ 000\ 000 - 10\ 000 = 990\ 000$ will be removed by the treatment.
Alternatively:
The shampoo will remove at least $99\%$ of the fleas.
$99\%$ of $1\ 000\ 000 = 990\ 000$.
Therefore, at least $990\ 000$ fleas will be removed by the treatment.