Problem 50 - Basic College Mathematics

Question

After Vivian completes \(60 \mathrm{hr}\) of teacher training in college, she can earn \(\$ 120\) for working a full day as a substitute teacher. How much will she receive for working \(\frac{3}{5}\) of a day?

Step-by-Step Solution

Answer

Vivian will earn \(\$ 72\) for working \(\frac{3}{5}\) of a day.

Step 1: Identify the Total Earnings for a Full Day

Vivian earns \(\$ 120\) for working a full day as a substitute teacher. This is the total amount she can earn in one day.

Step 2: Determine the Fraction of the Day Worked

Vivian works \(\frac{3}{5}\) of a day. This means she works only a part of the full day, specifically three-fifths of the entire day.

Step 3: Calculate the Earnings for the Fraction of the Day

To find out how much Vivian earns for \(\frac{3}{5}\) of a day, multiply her total earnings for a day by \(\frac{3}{5}\): \[ \$ 120 \times \frac{3}{5} = \$72 \]

Key Concepts

Teacher Training

Teacher training is a crucial step toward becoming a qualified educator. Vivian completes 60 hours of teacher training as part of her college curriculum. This training equips her with the necessary skills and knowledge to manage a classroom and deliver effective lessons. The training includes various aspects such as:

• Classroom management
• Lesson planning
• Interactive teaching methods
• Student assessment techniques

These skills are essential for ensuring that Vivian is well-prepared for the challenges of teaching. Completing the training also allows her to gain practical experience through internships or student teaching opportunities.

Part-Time Earnings Calculation

Understanding part-time earnings is important for managing finances effectively. Vivian earns $120 for a full day's work as a substitute teacher. Let's break down how to calculate her earnings if she works only part of the day.
First, identify the fraction of the day she works. In this case, Vivian works \(\frac{3}{5}\) of the day. Then, calculate her earnings by multiplying the total daily earnings by this fraction:

• Total earnings for a full day: \(\$120\)
• Fraction of the day worked: \(\frac{3}{5}\)
• Earnings for \(\frac{3}{5}\) of a day: \(\$120 \times \frac{3}{5} = \$72\)

Thus, Vivian will earn \(\$72\) for working \(\frac{3}{5}\) of a day. This calculation is essential for part-time workers who need to budget their income accordingly.

Multiplying Fractions

Multiplying fractions is a fundamental mathematical skill that can be applied in various real-life scenarios. To calculate earnings as in Vivian's case, we need to multiply a whole number by a fraction. Here's how to do it:

1. Identify the whole number and the fraction. For example, Vivian's total daily earnings of \(\$120\) (whole number) and the fraction of the day worked \(\frac{3}{5}\).
2. Convert the whole number to a fraction by placing it over 1: \(\$120 \times \frac{1}{1}\).
3. Multiply the numerators (top numbers) together and the denominators (bottom numbers) together:

• Numerator: 120 \(\times 3 = 360\)
• Denominator: 1 \(\times 5 = 5\)

4. Write the result as a fraction: \(\frac{360}{5}\).
5. Simplify the fraction if possible. In this case, 360 divided by 5 equals 72: \( \frac{360}{5} = 72\).
Hence, Vivian earns \(\$72\) for working \(\frac{3}{5}\) of a day. Understanding this process is key for solving similar problems involving fractions.