Problem:
If y varies directly as x, and y = 20 when x = 6, find x when y = 15.
Solution:
A direct variation is a relationship between two variables, x and y, that can be written as y = kx where k ≠ 0.
The statement, "y varies directly as x" translated into directly variation is y = kx where k is the constant of variation.
Solve if y is 20 and x is 6. So, find the constant using the equation of a combined variation.
- y = kx
- (20) = k(6)
- 20 = 6k
- 6k/6 = 20/6
- k = 10/3
The constant of the variation is 10/3. In equation of variation.
Find x when y is 15. Substitute the equation using the constant of the variation that you obtained.
- y = 10/3x
- (15) = 10/3x
- 15 × 3/10 = x
- x = 9/5 or 4.5
Answer:
∴ Therefore, the value of x is 9/5 or 4.5 to the directly variation.
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