If x varies directly as y, and if x = 6 when y = 15, find y when x = 30
6/15 = 30/Y
Solve for Y.
To solve this problem, we need to use the direct variation formula. In a direct variation, two variables are directly proportional, which means as one variable increases, the other also increases or as one variable decreases, the other also decreases. The direct variation formula is of the form:
x = ky
Where:
- x is the dependent variable
- y is the independent variable
- k is the constant of variation
In this case, x varies directly as y, so we can write the equation as:
x = ky
To find the constant of variation, we need to substitute the values given in the problem into the equation. We are given that when x = 6, y = 15. Let's substitute these values into the equation:
6 = k * 15
To solve for k, we divide both sides of the equation by 15:
6/15 = k
Simplifying the fraction gives us:
2/5 = k
Now that we have found the constant of variation (k = 2/5), we can use it to find y when x = 30. Let's substitute these values into the equation:
30 = (2/5) * y
To solve for y, we need to isolate it on one side of the equation. We can do this by multiplying both sides of the equation by 5/2:
30 * (5/2) = (2/5) * y * (5/2)
This simplifies to:
75 = y
Therefore, when x = 30, y = 75.