On Monday, a dental hygienist cleans teeth of 5 patients by the time she takes her lunch break at noon. On average, she is able to clean the teeth of 9 patients in 4 hours.

Question

Write a function to represent the number of patients she sees, y , and the number of hours,x , the hygienist works after lunch on Monday.

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Answer 1

To represent the relationship between the number of patients she sees (y) and the number of hours she works after lunch (x), we need to determine her cleaning rate.

From the problem, we know that:

• She cleans 9 patients in 4 hours.

We can calculate her rate of cleaning patients per hour:

\[ \text{Rate} = \frac{9 \text{ patients}}{4 \text{ hours}} = 2.25 \text{ patients/hour} \]

This means for every hour she works, she cleans 2.25 patients.

Now, since she already cleaned 5 patients before lunch, the total number of patients she will see after lunch can be represented by the equation:

\[ y = 5 + 2.25x \]

where:

• \( y \) is the total number of patients she sees,
• \( x \) is the number of hours she works after lunch.

So, the function can be written as:

\[ y = 5 + 2.25x \]