A store sold a combined total of 480 history and sociology books in a week. the number of sociology books sold was 50 less than the number of history books. how many books of each type were soled?s?

Answer 1

Hi there!

Here, it looks like we have a typical constraint problem. In these kinds of problems, we can construct as many constraint equations as there are variables in the equation. The two variables in this problem would be the number of history books and the number of sociology books – let's denote them x and y, respectively.

First, we're told that the number of history and sociology books combined is 480. From this, we can make our first equation: the total number of books has to be 480, so we can write

x + y = 480

If this were all the information we had, then there would be an infinite number of solutions to the problem. However, in this problem we're given extra information from which we can make a second equation.

We're then told that 50 less sociology books were sold than history books. Remembering that history books are x and sociology books are y, we can additionally write

y = x - 50

We now have our two equations to work with. From here, we can substitute the value of y in the second equation into our y in the first equation:

(1) x + y = 480

(2) y = x - 50

(2) -> (1) x + (x - 50) = 480

From here, we can then solve for x:

(1) x + x - 50 = 480

(2) 2x - 50 = 480

(3) 2x = 530

(4) x = 265

This gives us the number of history books: 265.

With this new value for x, we can then determine the value of y (sociology books) from our first equation:

(1) x + y = 480

(2) x = 265

(3) 265 + y = 480

(4) y = 215

So from this, we get that 215 sociology books were sold.

Let's check our work, and make sure it all adds up correctly. We got that 265 history books and 215 sociology books were sold.

265 + 215 = 480, so that satisfies the first constraint;

265 is 50 more than 215, so that satisfies the second constraint. So, we're done!

I hope this helped and gave you a better understanding of how to solve these kinds of constraint problems!

Answer 2

Total books sold = history books sold + sociology books sold

Let x = the number of history books sold

Given info: sociology books sold is 50 less than history books sold,

therefore, let x – 50 = the number of sociology books sold

Substitute the variables into the equation above:

Total books sold = history books sold + sociology books sold

480 = x + (x – 50)

480 = 2x – 50

480 + 50 = 2x – 50 + 50 (add 50 to each side to combine the integers)

530 = 2x (divide both sides by 2)

530/2 = x

265 = x

So there were 265 history books (x) and 215 sociology books (x-50) sold