Problem 88 - Elementary Algebra

Question

A community has 37,500 low-wage workers. Predict how many do not receive paid sick days. Three out of four low-wage workers in the private sector do not have employer- provided health insurance, while eight out of nine do not participate in a pension plan. Three-fourths of low-wage workers do not receive paid sick days, so if they need to miss two days work because they are sick or their child is sick, they receive no pay for those days and of ten risk getting fired. (Source: Greenhouse, Steven, The Big Squeeze: Tough Times for the American Worker, Knopf, 2008)

Step-by-Step Solution

Answer

28,125 workers do not receive paid sick days.

Step 1: Identify the total number of low-wage workers

The problem states that there are 37,500 low-wage workers in the community.

Step 2: Determine the fraction of workers who do not receive paid sick days

The problem mentions that three-fourths (or \(\frac{3}{4}\)) of low-wage workers do not receive paid sick days.

Step 3: Calculate the number of workers who do not receive paid sick days

Multiply the total number of low-wage workers (37,500) by the fraction who do not receive paid sick days (\(\frac{3}{4}\)) to find the number of workers without paid sick days: \(37,500 \times \frac{3}{4} = 28,125\)

Key Concepts

Fractions in Algebra

Fractions are an essential part of algebra and everyday math. In this problem, we use the fraction \(\frac{3}{4}\) to determine a portion of low-wage workers who do not receive paid sick days. A fraction consists of two numbers: the numerator (top number) and the denominator (bottom number). The numerator represents the number of parts of the whole, and the denominator shows how many equal parts make up that whole. Here, \(\frac{3}{4}\) means there are three parts out of a total of four.
Understanding fractions is crucial for solving many algebra problems, especially those involving parts of a whole, like percentages and ratios. To work with fractions in algebra:

• Ensure you properly interpret the fraction's meaning in context.
• Convert fractions to decimals if necessary for easier calculations.
• Use fraction multiplication and division to find parts of quantities.

In our problem, we successfully identified that to find the number of low-wage workers without paid sick days, we can multiply the total number of workers by the given fraction.

Multiplication

Multiplication is a fundamental arithmetic operation used to calculate the total amount when combining equal groups. In this problem, we use multiplication to find how many of the 37,500 low-wage workers do not receive paid sick days.
When we multiply, we combine numbers to determine the total amount. Here, the goal is to calculate the total number of workers without paid sick days by multiplying the fraction \(\frac{3}{4}\) with the total number of workers (37,500).
The formula used is:
\[ Total \ Number \ of \ Workers \times Fraction \]Plugging in the values, we get:
\(37,500 \times \frac{3}{4} = 28,125\)
This means 28,125 low-wage workers do not receive paid sick days. Understanding multiplication helps simplify complex problems into clear, actionable steps. Always ensure accuracy in your calculations by performing the steps methodically and checking your work.

Worker Benefits

Worker benefits are essential aspects of employment that significantly affect workers' quality of life. In many cases, especially among low-wage workers, benefits like paid sick days, health insurance, and pension plans are not provided. This problem highlights the situation where three-fourths of low-wage workers do not receive paid sick days.
Benefits are critical for a few reasons:

• Provide financial security during illness or emergencies, reducing worker stress.
• Encourage employee loyalty and reduce turnover rates.
• Promote overall well-being, leading to a healthier, more productive workforce.

Unfortunately, many workers in lower-wage jobs, as the problem demonstrates, lack these essential benefits.
This can lead to significant hardships, such as not having income when they or their family members are sick, which can also increase the risk of job loss. Recognizing the importance of worker benefits aids in understanding broader social and economic issues, contributing to a deeper awareness of employment policies and their impact on society.