Example Card: Solving a Word Problem with Direct Variation
Master Solving a Word Problem with Direct Variation with step-by-step worked examples for Grade 9 math students. Practice identifying key patterns and apply techniques to solve problems accurately.
Key Concepts
Let's use direct variation to solve a real world problem about earnings and hours worked. We will use the second key idea, Writing and Solving a Direct Variation Equation, to solve this problem.
Example Problem The amount of money earned varies directly with the hours worked. If a person earns 90 dollars in 6 hours, how much will they earn in 10 hours?
Step by Step 1. First, we establish that the money earned, $y$, varies directly with the hours worked, $x$. The given point is $(6, 90)$. 2. Begin with the general equation for direct variation: $$y = kx$$ 3. Substitute the values from the known point to find the constant of variation, $k$. $$90 = k \cdot 6$$ 4. Solve for $k$ by dividing both sides by 6. $$k = 15$$ 5. Now, write the specific direct variation equation for this relationship. $$y = 15x$$ 6. Use this equation to find the earnings for 10 hours by substituting $10$ for $x$. $$y = 15 \cdot 10$$ 7. Simplify to find the answer. The person will earn 150 dollars. $$y = 150$$.
Common Questions
What is Solving a Word Problem with Direct Variation in Grade 9 math?
Solving a Word Problem with Direct Variation is a key algebra concept where students learn to apply mathematical rules and properties to solve problems. Understanding this topic builds skills needed for higher-level math.
How do you solve problems involving Solving a Word Problem with Direct Variation?
Identify the given information, apply the relevant property or formula, simplify step by step, and check your answer. Practice with varied examples to build fluency.
Where is Solving a Word Problem with Direct Variation used in real life?
Solving a Word Problem with Direct Variation appears in fields like science, engineering, finance, and technology. Understanding this concept helps solve real-world problems that involve mathematical relationships.