Let us draw a Venn diagram for this question:

We denote percentage of people who liked both candidates A and B by

*x*. Then the percentage of people who liked only one candidate is 2

*x*. The sum of these numbers is the percentage of people who liked at least one candidate. 3

*x*.

On the other hand, the percentage of people who liked at least one candidate can be calculated as

30% + 48% –

*x* = 78% –

*x*.

Therefore we get equation:

78% –

*x* = 3

*x*We can also construct an equation in a different way

If we denote percentage of people who liked both candidates A and B by

*x* then we can calculate percentages of people who liked only A or only B. The sum of these numbers is

(30% –

*x*) + (48% –

*x*) = 78% – 2

*x*It must be equal to 2

*x*. Therefore we get an equation:

78% – 2

*x* = 2

*x*We can see that it is the equivalent equation to the one that is in the explanation.