A textbook store sold a combined total of 475 sociology and history textbooks in a week. The number of history textbooks sold was 83 less than the number of sociology textbooks sold. How many textbooks of each type were sold?

Let the number of Sociology books = y; the number of History books = x

⇒ x + y = 475 (2)

also since the number of history books sold was 83 less than sociology,

then x = y - 83 (1)

BY substituting (1) into (2)

⇒ (y - 83) + y = 475

2y = 475 + 83

y = (558 : 2)

y = 279

⇒ x = 279 - 83

x = 196

∴ Number of History books is 196 & number of Sociology books is 279.