Find the value of y for a given value of x, if y varies directly with x.
If y=252 when x=84, what is y when x=74?
If y varies directly with x, this means that the ratio of y to x is constant.
We can use this information to set up a proportion:
y/x = 252/84
To find y when x=74, we can set up a new proportion using the same ratio:
y/74 = 252/84
Now, we can cross-multiply and solve for y:
84y = 74 * 252
84y = 18,768
y = 18,768/84
y = 223
Therefore, when x=74, y=223.
To find the value of y when x=74, we can use the concept of direct variation. In direct variation, two variables are directly proportional to each other, meaning that as one variable increases or decreases, the other variable changes in the same proportion.
To solve this problem, we need to find the constant of variation (k) and then use it to find the value of y when x=74.
Given that y=252 when x=84, we can set up the equation:
y = kx
Substituting the given values, we have:
252 = k * 84
To find the value of k, we can solve for it by dividing both sides of the equation by 84:
k = 252 / 84
k = 3
Now that we have the value of k, we can use it to find the value of y when x=74:
y = kx
y = 3 * 74
y = 222
Therefore, when x=74, y will be equal to 222.
If y varies directly with x, it means that y and x are proportional to each other. This can be represented by the equation y = kx, where k is the constant of proportionality.
To find the value of k, we can use the given information: when x = 84, y = 252. Substituting these values into the equation, we have 252 = k * 84.
To find the value of k, we divide both sides of the equation by 84: k = 252 / 84 = 3.
Now that we know the value of k, we can find y when x = 74. We substitute the values into the equation: y = 3 * 74.
Evaluating the equation, we have y = 222.
Therefore, when x = 74, y = 222.