Combining Direct and Indirect Variations in Solving for Unknown Variables

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To solve for the unknown variable t when s varies directly as r and inversely as t, the relationship can be expressed as s = k(r/t). Given s = 10 when r = 5 and t = 3, the constant k can be determined. The challenge lies in combining direct and indirect variations into a single equation. By substituting the known values into the equation, one can derive the value of t when s = 3 and r = 4. Understanding how to consolidate these variations is essential for solving such problems effectively.
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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 k rather than two separate expressions.
 


Got it, thanks.
 

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