To solve the problem where x varies directly as y, we can use the concept of direct variation. Direct variation can be expressed with the equation:
x = k * y
In this equation, k is a constant that defines the relationship between x and y. We need to first determine the value of k using the initial condition provided: when y is 9, x is 153.
Let’s substitute these values into the equation:
153 = k * 9
To find the value of k, we divide both sides by 9:
k = 153 / 9 = 17
Now we have determined that k = 17. The relationship between x and y can be expressed as:
x = 17 * y
Next, we will find the value of x when y is 13. We can substitute 13 into the equation:
x = 17 * 13
Now, performing the multiplication:
x = 221
Therefore, when y is 13, the value of x is 221.