Math Problem Statement
If xx and yy are in direct proportion and yy is 10 when xx is 2, find yy when xx is 6.
Solution
If and are in direct proportion, we can express the relationship as:
where is the constant of proportionality.
We are given that when . Substituting these values into the equation to find :
Now, we are asked to find when . Using the same relationship:
Solving for :
Thus, when , .
Would you like more details or further explanations?
Here are some related questions for further exploration:
- What is the constant of proportionality in general terms for this kind of problem?
- How does the solution change if the relationship were inverse instead of direct?
- Can you determine instead of given the same conditions?
- How would the equation look if we introduced a constant multiplier in ?
- What happens to if is doubled?
Tip: In problems involving direct proportion, once you know the proportionality constant, you can solve for unknowns by multiplying or dividing appropriately.
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Math Problem Analysis
Mathematical Concepts
Direct Proportion
Algebra
Formulas
x^2 ∝ y^2 (Direct Proportion Relationship)
k = x^2 / y^2 (Proportionality Constant)
Theorems
Direct Proportionality Theorem
Suitable Grade Level
Grades 6-8
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