Final answer:
To solve this problem, set up a system of equations based on the given information. The number of sociology books sold is 240 and the number of physics books sold is 179.
Step-by-step explanation:
To solve this problem, we can set up a system of equations based on the given information. Let's say the number of sociology books sold is x. According to the problem, the number of physics books sold is 61 less than the number of sociology books sold, so the number of physics books sold is x - 61.
We know that the combined total of sociology and physics books sold is 419, so we can set up the equation x + (x - 61) = 419.
Simplifying this equation, we get 2x - 61 = 419. Adding 61 to both sides of the equation, we have 2x = 480. Dividing both sides by 2, we find that x = 240.
Therefore, the number of sociology books sold is 240, and the number of physics books sold is 240 - 61 = 179.