Video: AQA GCSE Mathematics Foundation Tier Pack 2 • Paper 2 • Question 15

Hugo and Sofia played games in an arcade. For Hugo, his ratio of wins to losses was 1 : 8. For Sofia, her ratio of wins to losses was 1 : 9. Sofia says, “Since 9 is greater than 8, I lost more games than Hugo.” Give an example to show that Sofia could be incorrect.

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Video Transcript

Hugo and Sofia played games in an arcade. For Hugo, his ratio of wins to losses was one to eight. For Sofia, her ratio of wins to losses was one to nine. Sofia says, “Since nine is greater than eight, I lost more games than Hugo.” Give an example to show that Sofia could be incorrect.

We have to remember that these ratios do not tell us the exact number of wins and losses, just the proportion of wins to losses. We need to give an example to show that what Sofia said could be incorrect. Sofia says that since nine is greater than eight, she lost more games than Hugo.

Hugo’s ratio of wins to losses is one to eight, and Sofia’s ratio is one to nine. If Sofia had won one game, then she would’ve lost nine games. In addition to that, if Hugo had won two games, he would have lost 16 games. Since his ratio must be one to eight, if Hugo won two games, he would’ve lost eight times two games, 16 games total.

In this scenario, Hugo has lost 16 games and Sofia has only lost nine games. 16 is greater than nine. In this example, Sofia has lost less games than Hugo.

These two statements provide a counterexample to Sofia’s statement. And this comparison confirms what we’ve already said. There are many other possible examples. However, to disprove Sofia’s statement, we only need to find one counterexample.

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