Combining Direct and Indirect Variations in Solving for Unknown Variables

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In summary, s varies directly as r and inversely as t. When s=10, r=5, and t=3. To find the value of t when s=3 and r=4, we can use the formula s=kr=k/x. However, in order to combine the direct and indirect variations, we need to write everything as a single variation using only one constant k. This will allow us to solve for t in the end.
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Homework Statement


s varies directly as r and inversely as t. s=10 when r=5 and t=3. What value of t will s=3 and r-4?

Homework Equations


Direct variation: y=kx; Indirect variation: y=k/x

The Attempt at a Solution


I tired s=kr=k/x and plugging in the given, but I could not get t in the end.

My real question is how to combine variations, meaning: because s varies directly AND inversely, how do you combine the variations?
 
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Write everything as a single variation, using only one constant [itex] k [/itex] rather than two separate expressions.
 
  • #3


Got it, thanks.
 

FAQ: Combining Direct and Indirect Variations in Solving for Unknown Variables

What is a single variation in math?

A single variation in math refers to a mathematical expression or equation that contains only one variable. This means that the equation or expression can be solved for that one variable, and all other variables are considered constants.

Why is understanding single variation important in math?

Understanding single variation in math is important because it allows us to solve problems involving only one variable. This is useful in many real-world applications, such as calculating rates, determining the relationship between two quantities, and predicting outcomes.

How do I solve a single variation equation?

To solve a single variation equation, you can use algebraic methods such as simplifying, factoring, or isolating the variable on one side of the equation. You may also need to use properties of equality and inverse operations to manipulate the equation and solve for the variable.

What are some common examples of single variation problems?

Some common examples of single variation problems include calculating distance, rate, and time; solving for missing angles in geometric figures; and determining the relationship between two quantities, such as cost and quantity or price and demand.

How can I practice solving single variation problems?

You can practice solving single variation problems by working through examples in textbooks or online resources, creating your own practice problems, and participating in math competitions or challenges. You can also seek help from a tutor or join a study group to improve your skills.

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