Washing-up
What fraction of customers buy Kleenz after the advertising campaign?
Age
14 to 16
Challenge level
Problem
A survey for washing-up liquid revealed that $\frac{2}{3}$ of all customers bought Jinx and $\frac{1}{3}$ of customers bought Kleenz. Nobody bought both.
After an advertising campaign for Kleenz, the only change in sales was that $\frac{1}{4}$ of the people who had bought Jinx were now buying Kleenz instead.
What fraction of customers now buy Kleenz?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
Answer: $\frac12$
The fraction of customers that now buy Kleenz is the $\frac{1}{3}$ that bought it originally, plus $\frac{1}{4}$ of the $\frac{2}{3}$ that bought Jinx originally.
Therefore the overall fraction is:
$\frac{1}{3} + \frac{1}{4} \times \frac{2}{3} = \frac{1}{3} + \frac{1}{6} = \frac{1}{2}$