Chapter 2.4, Problem 18E

Performance on Tests A teacher estimates that, of the students who pass a test, 80% will pass the next test, while of the students who fail a test, 50% will pass the next test. Let x and y denote the number of students who pass and fail a given test, and let u and v be the corresponding numbers for the following test.

(a) Write a matrix equation relating $\left[\begin{array}{c}x\\ y\end{array}\right]$ to $\left[\begin{array}{c}u\\ v\end{array}\right]$.

(b) Suppose that 25 of the teacher’s students pass the third test and 8 fail the third test. How many students will pass the fourth test? Approximately how many passed the second test?