Question

Alan took a total of 42 quizzes over the course of 7 weeks. How many weeks of school will Alan have to attend this quarter before he will have taken a total of 60 quizzes? Solve using unit rates.

Answer 1

We can set up a ratio to represent the number of weeks Alan will attend for 60 quizzes. Let's call the number of weeks Alan will have to attend $x$. The ratio is $\frac{x \text{ weeks}}{60 \text{ quizzes}}$.
Similarly, we can set up a second ratio to represent the number of weeks Alan attended for 42 quizzes. This ratio is $\frac{7 \text{ weeks}}{42 \text{ quizzes}}$.
Since the number of weeks Alan attended is directly proportional to the number of quizzes, we can set up the following proportion:
$$\frac{x}{60}=\frac{7}{42}$$
To find $x$, we cross-multiply and solve for $x$:
$$42 \cdot x = 7 \cdot 60$$
$$42\cdot x = 420 $$
$$\frac{42 \cdot x}{42}=\frac{420}{42}$$
$$x = 10$$
Therefore, Alan will have to attend 10 weeks of school before he will have taken a total of 60 quizzes.