Math Problem Statement
Solution
To solve this, let's break down the problem:
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Problem Analysis:
- Stan earns $7.25 per hour during the day (represented by ) and $9.25 per hour at night (represented by ).
- Stan wants to earn a total of $300.
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Setting Up the Equation: The total earnings equation is:
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Finding the Graph Representation: We can rearrange the equation to find the intercepts:
- For the -intercept (when ):
- For the -intercept (when ):
These intercepts give us the points and , which should appear on the correct graph.
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Identifying the Correct Graph: Look for a graph with intercepts near and , and that aligns with the negative slope expected from the equation.
The correct graph should be the one where:
- The -axis intercept is approximately at 41.
- The -axis intercept is approximately at 32.
Do you want further explanation on setting up and solving linear equations like this?
Related Questions
- How would the graph change if the total earnings target was $400 instead?
- What would the equation look like if Stan was paid $8 during the day and $10 at night?
- How many hours would Stan need to work only at night to earn $300?
- If Stan wanted to split his hours equally between day and night, how would his earnings equation change?
- How can we determine if a solution exists for a given earnings goal and hourly rates?
Tip: Always start by identifying intercepts when graphing linear equations with two variables—this simplifies plotting the line quickly.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Graphing
Formulas
7.25x + 9.25y = 300
Theorems
Linear Equation Intercepts
Suitable Grade Level
Grades 9-10
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