The number of wrecks at a certain intersection varies directly as the number of cars that travel through the intersection. If there are 31 wrecks when 1,085 cars have traveled through the intersection, how many cars have passed through the intersection after 7 wrecks?
If the number of wrecks varies directly as the number of cars that travel through the intersection, then we can write the relationship as:
wrecks = k * cars
where k is a constant of variation.
We are given that when 1,085 cars have traveled through the intersection, there are 31 wrecks. Substituting these values into the equation above, we get:
31 = k * 1085
To find the value of k, we can divide both sides of the equation by 1085:
k = 31 / 1085 = 0.028571429
Now we can use this value of k to find how many cars have passed through the intersection after 7 wrecks. Substituting the values into the equation, we get:
7 = 0.028571429 * cars
To solve for cars, we can divide both sides of the equation by 0.028571429:
cars = 7 / 0.028571429 = 245
Therefore, 245 cars have passed through the intersection after 7 wrecks.