Question

A textbook store sold a combined total of 365 sociology and history textbooks in a week. The number of history textbooks sold was 71 less than the number of sociology textbooks sold. How many textbooks of each type were sold?

Answer 1

By setting up a system of linear equations based on the information given, it is calculated that the store sold 218 sociology textbooks and 147 history textbooks.

Step-by-step explanation:

The question involves solving a system of linear equations to find out how many sociology and history textbooks were sold. Let's define the variables: let s represent the number of sociology textbooks sold and h represent the number of history textbooks sold. According to the problem, s + h = 365, and the number of history textbooks sold was 71 less than the number of sociology textbooks, which gives us h = s - 71.

To find the number of sociology textbooks sold, we'll substitute the second equation into the first: s + (s - 71) = 365. This simplifies to 2s - 71 = 365. Solving for s, we get:

• 2s - 71 = 365
• 2s = 365 + 71
• 2s = 436
• s = 436 / 2
• s = 218

Now that we know that 218 sociology textbooks were sold, we can find the number of history textbooks by substituting s back into the second equation: h = 218 - 71, which gives us:

• h = 147

Therefore, the store sold 218 sociology textbooks and 147 history textbooks.