hey i needs help
Suppose y varies directly with x, and y = 25 when x = 140. What is the value of x when y = 36?
Can you show my how to solve this step-by-step?
Of course! To solve this problem, we can use the concept of direct variation. In direct variation, two variables, such as x and y, are said to vary directly if their ratio remains constant.
Step 1: Identify the given information:
- We are told that y varies directly with x.
- When x = 140, the corresponding value of y is 25.
Step 2: Set up the direct variation equation:
The equation for direct variation is given in the form y = kx, where k is the constant of variation.
Step 3: Determine the value of k:
Using the given information, we can substitute x = 140 and y = 25 into the equation:
25 = k * 140
To find k, divide both sides of the equation by 140:
k = 25/140
Simplifying the fraction, we get:
k = 5/28
So, the constant of variation is k = 5/28.
Step 4: Use the direct variation equation to find x:
Now that we have the constant of variation, we can solve for x using the equation y = kx.
Substitute y = 36 and k = 5/28 into the equation:
36 = (5/28) * x
To solve for x, multiply both sides of the equation by 28/5:
(28/5) * 36 = x
Simplifying the expression:
x = 201.6
Therefore, when y = 36, the corresponding value of x is 201.6.
I hope this step-by-step explanation helps! Let me know if you have any further questions.