Question

Jeanne babysits Chuy one day each week. Jeanne charges a $$\mathrm{\$}20$$ fee for the day, plus $$\mathrm{\$}5.50$$ for every 30 minutes of babysitting. How much has Jeanne earned after three hours of babysitting? (Disregard the $$$ sign when gridding your answer.)

Short answer

Jeanne has earned $53$ after three hours of babysitting.

Step-by-step solution

Convert time to minutes

First, we will convert the given time of three hours into minutes: $1\text{ hour}=60\text{ minutes}$ So, $3\text{ hours}=3\times 60=180\text{ minutes}$.

Determine the number of 30-minute increments

Now that we have the total number of minutes in three hours, we need to find out how many 30-minute increments are in 180 minutes. To do this, divide the total minutes by 30: $\frac{180\text{ minutes}}{30\text{ minutes}}$ = $6$ increments of 30 minutes.

Calculate earnings from 30-minute increments

We know that Jeanne charges $5.50 for every 30 minutes of babysitting. Since there are 6 increments of 30 minutes in 3 hours, the earning from babysitting for 3 hours would be $$5.50\times 6$$.

Calculate total earnings

The total earnings would be the sum of the $20 fixed fee and the earnings from the 30-minute increments. So, Jeanne's total earnings after babysitting for three hours would be $$20+(5.50\times 6)$$.

Evaluate the expression

Now, we will evaluate the expression to find the total earnings: $$20+(5.50\times 6)=20+33=53$$. Jeanne has earned $$\mathrm{\$}53$$ after three hours of babysitting. (Disregard the $$$ sign when gridding your answer.)

Key concepts

Babysitting Math Problem

Tackling a babysitting math problem requires understanding a mix of flat fees and per-time-unit charges. In the practice problem, we have Jeanne babysitting Chuy, with her earnings being a combination of a daily flat fee and an additional charge per half-hour. It's important to understand that these kinds of problems are essentially two-part rate problems. Firstly, we have a flat rate that doesn't change with time—the $20 day fee in this case. Secondly, there's a variable rate, depending on the time spent babysitting.

To solve this problem, students must do the following: Identify the fixed fee, calculate the total time spent babysitting in the preferred time unit (e.g., minutes or hours), and then use the per-time-unit charge to calculate the variable portion of the earnings. After summing the flat fee and the variable earnings, they will have the total amount earned. This practical approach can help with various real-life scenarios, like babysitting, tutoring, or part-time jobs with similar wage structures. Remember, breaking down the problem into manageable steps is key to solving it efficiently.

Calculating Earnings

When it comes to calculating earnings, especially in problems that involve separate rates for a service, we utilize simple multiplication and addition. The first step is always to calculate the separate parts of the earnings. In Jeanne's case, we consider her fixed daily fee and the rate per half-hour of babysitting. After determining the number of time units worked (here, half-hour increments), students should multiply this number by the per-unit rate. To ensure thorough understanding:

• The fixed fee is always added as it is, and doesn't depend on the time spent working.
• The variable fee is directly proportional to the number of time units worked and is calculated accordingly.

This concept can be applied beyond babysitting to calculate earnings in various job scenarios, such as freelance projects, piecework, or other tasks with combined fixed and hourly rates. It provides an essential foundation in personal finance and business calculations.

Time Conversion to Minutes

The problem often encountered in math related to jobs and services is the need for time conversion to minutes. Many rates are given per hour or per some fraction of an hour, making it essential to be comfortable with converting hours to minutes and vice versa. Here's how to do it in easy steps:

• Remember that 1 hour equals 60 minutes.
• To convert hours to minutes, multiply the number of hours by 60.
• For reverse conversion, divide the number of minutes by 60 to get the amount in hours.

For our problem, the time Jeanne spent babysitting needed to be converted into 30-minute increments. This process allowed us to calculate her variable earnings with precision. Mastery of converting time units is not only useful in answering math problems but also a valuable skill for everyday activities, such as cooking, time management, and travel planning.