Mason read a total of 6 books over 3 months. If Mason has read 36 books so far, how many months has he been with his book club? Assume the relationship is directly proportional.
Understand the Problem
This is a word problem involving direct proportion. We know Mason reads 6 books every 3 months and has read 36 books total. The question asks us compute how long Mason has been in the book club in months.
Answer
18 months
Answer for screen readers
Mason has been in the book club for 18 months.
Steps to Solve
- Find Mason's reading rate
To find Mason's reading rate, we need to determine how many books he reads per month. We know he reads 6 books every 3 months, so we can divide the number of books by the number of months.
$\frac{6 \text{ books}}{3 \text{ months}} = 2 \text{ books per month}$
- Calculate the total time in the book club
Now that we know Mason reads 2 books per month and has read 36 books in total, we can divide the total number of books by his reading rate to find the total time he's been in the book club.
$\frac{36 \text{ books}}{2 \text{ books per month}} = 18 \text{ months}$
Mason has been in the book club for 18 months.
More Information
Direct proportion problems can often be solved using ratios or rates. In this case, understanding the rate at which Mason reads books is critical for solving the problem.
Tips
- Incorrectly setting up the rate: A common mistake is to invert the rate, calculating months per book instead of books per month. This would lead to an incorrect final answer.
- Misunderstanding the units: It is important to keep track of the units (books and months) to ensure the final answer is in the correct unit (months).
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