Math Problem Statement
Suppose y varies jointly with x and z. If y = 20 when x = 2 and z = 5, find the constant k. Then find y when x = 4 and z = 8.
Solution
From the image, the problem states:
"Suppose varies jointly with and , i.e.,
.
If when and , find .
Then find when and ."
Step 1: Solve for
We use the equation . Plugging in the given values:
Simplify:
Thus, .
Step 2: Find when and
Using and the equation :
Simplify:
Final Answer:
- when and .
Would you like a detailed explanation of any step?
Related Questions:
- What is joint variation, and how does it differ from direct variation?
- How can you determine the constant of proportionality () in other joint variation problems?
- If and , what is when and ?
- How can the formula for joint variation be modified for inverse relationships?
- What happens to if doubles and remains the same?
Tip:
Always isolate the constant first in variation problems—it helps simplify the rest of the solution!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Joint Variation
Algebra
Formulas
y = kxz
Theorems
Variation Principle
Suitable Grade Level
Grades 8-10