Final answer:
The value of y varies directly with x. When y = 55, x = 12. To find the value of y when x is 314, we can use the equation y = kx and solve for k. Once we have k, we can substitute it into the equation to find the value of y.
Step-by-step explanation:
Given that the value of y varies directly with x, we can write the equation y = kx, where k is the constant of variation.
To find the value of y when x is 314, we can use the given values of y and x to find the value of k.
Using the equation y = kx, when y = 55 and x = 12, we can solve for k: 55 = 12k. Dividing both sides by 12 gives us k = 4.58.
Now that we have the value of k, we can substitute it into the equation to find the value of y when x = 314: y = 4.58(314). Simplifying this equation gives us y = 1432.12.