Question

65 people took a clarinet exam. Before the exam, 23 people predicted that they would pass, and the rest predicted they would fail. Of the people who predicted they would pass, 18 actually did. In total, 31 people passed the clarinet exam. What fraction of those who thought that they would fail actually did fail?​

Answer 1

Answer:

The answer is 29/42

Step-by-step explanation:

First, let's calculate how many people predicted they would fail. The question states that 65 people took the exam and 23 predicted they would pass, so we can find the number of people that predicted they would fail by the following calculation:

Let FP be the people who predicted they'd fail

65 = 23 + FP

65 - 23 = FP

42 = FP

Now, let's move on to the next part. The question states that a total of 31 people passed the test, from those 18 being the people who predicted they would pass and the rest are people who had predicted they would fail but ended up passing.

Let's set x as the number of people who predicted they would fail but have passed.

31 = 18 + x

31 - 18 = x

13 = x

Since 13 of the 42 FP have passed, we can calculate how many of them failed. Let y be the number of people that predicted to fail and ended up failing:

13 + y = 42

y = 42 - 13

y = 29

Finally, now we have the fraction of those who predicted that they would fail actually did fail and that's 29/42