James buys 4 tickets in a raffle. If his chances of winning are 1/125, how many tickets have been sold?

1 answer

Let \( x \) be the total number of tickets sold in the raffle. James buys 4 tickets, and the probability of winning with those tickets is given by the formula:

\[ \text{Probability of winning} = \frac{\text{Number of tickets bought}}{\text{Total number of tickets sold}} = \frac{4}{x} \]

According to the problem, his chances of winning are \( \frac{1}{125} \). Setting the two expressions equal gives us:

\[ \frac{4}{x} = \frac{1}{125} \]

To find \( x \), we can cross-multiply:

\[ 4 \cdot 125 = 1 \cdot x \]

Calculating \( 4 \cdot 125 \):

\[ 4 \cdot 125 = 500 \]

Thus, we have:

\[ x = 500 \]

So, the total number of tickets sold is

\[ \boxed{500} \]