If y varies directly as x and y=3 when x=10, find x when y=8? Can you please show me step by step solution for this problem?
Whenever you have a statement such like yours,
"If y varies directly as x "
you can form the equation
y = kx , where k is a constant
sub in the given: y=3 , x=10 to find k
3 = k(10)
k = 3/10
so your equation is y = (3/10)x
then when y = 8
8 = (3/10)x
80 = 3x
x = 80/3
btw, if it has said" y varies inversely as x" your equation would have been
y = k(1/x), but you would follow the same steps of subbing in the given data to find k
Thank you so much that helps a lot!
welcome
Sure, let's solve this problem step by step in a humorous way:
Step 1: Establish the given information.
We know that "y varies directly as x," which basically means there's some constant relationship going on between them. So we can say y = kx, where k is the constant of variation we need to find.
Step 2: Use the given values to find k.
We are told that when x = 10, y = 3. Plugging these values into our equation, we get 3 = k * 10. To find k, divide both sides by 10. So, k = 3/10.
Step 3: Insert the value of k into the equation.
Now that we have the value of k, we can use it to find x when y = 8. Let's call this unknown x as "x2". Plugging in the values, we have 8 = (3/10) * x2.
Step 4: Solve for x2.
To find x2, we can multiply both sides by 10/3, which is the reciprocal of 3/10. This cancels out the fraction nicely. So, 8 * (10/3) = x2. Simplifying this, we get x2 ≈ 26.7 (approximately).
So, when y = 8, x is approximately 26.7. Keep in mind that this was a direct variation problem, and approximation is used due to the decimals involved. I hope this humorous explanation helped make the solution more entertaining for you!
To find x when y=8 in a direct variation equation, we can use the formula for direct variation, which is y = kx. Here's how to solve it step by step:
Step 1: Write down the direct variation equation: y = kx.
Step 2: Plug in the given values from the problem: y=3 when x=10. So we have 3 = k(10).
Step 3: Solve the equation for k. Divide both sides of the equation by 10: 3/10 = k.
Step 4: Calculate the value of k. 3/10 = 0.3.
Step 5: Now that we have k = 0.3, we can use this value to find x when y = 8.
Step 6: Substitute the values into the direct variation equation: 8 = 0.3x.
Step 7: Isolate x by dividing both sides of the equation by 0.3: x = 8/0.3.
Step 8: Perform the division: x = 26.6666... (rounded to the nearest tenth, it is approximately 26.7).
Therefore, when y = 8, x would be approximately 26.7.