- Identify the variables: the earnings from washing cars is \$32 and the earnings from mowing lawns is \(m\).
- Translate the relationship "twice as much" into an equation: \(2 \times m = 32\).
- Match the equation with the provided options, which confirms the correct choice is \(2m = 32\).
- The final answer is \(\boxed{2m = 32}\).
Explanation
- Problem Analysis
We are given that Greg earned \(\$32\) for washing cars this month. Let \(m\) be the amount of money he earned for mowing lawns. The problem states that he earned twice as much for washing cars than he did for mowing lawns. We need to express this relationship as an equation to solve for \(m\).
- Formulating the Equation
The amount earned for washing cars is \(\$32\). The amount earned for mowing lawns is \(m\). Since the amount from washing cars is twice the amount from mowing lawns, we can represent this as:
\(\text{Amount from washing cars} = 2 \times (\text{Amount from mowing lawns})\)
Substituting the given values, we get:
\(32 = 2 \times m\)
This can also be written as \(2m = 32\).
- Identifying the Correct Option
Comparing our derived equation \(2m = 32\) with the given options:
- \(2m = 32\)
- \(m + 2 = 32\)
- \(m - 2 = 32\)
- \(\frac{m}{2} = 32\)
The correct equation is \(2m = 32\).
Examples
Equations like this are used in budgeting and resource management. For example, if you know the total cost of a project and how one component relates to another in terms of cost (e.g., "the painting costs twice as much as the framing"), you can set up an equation to find the exact cost of each part. This simple algebraic modeling is a fundamental skill for financial planning and everyday problem-solving.