Question

A textbook store sold a combined total of 464 physics and history textbooks in a week. the number of physics textbooks sold was three times the number of history textbooks sold. how many textbooks of each type were sold?

Answer 1

Let H = the number of history books sold in the store. Let P = the number of physics books.The problem says "three times as many physics books are sold", so we can set two equations in two variables that describe this scene. Equation 1 writes the second sentence; Equation 2 writes the third sentence

`Equation 1: H + P = 464`

`Equation 2: P = 3H.`

We then solve this two-by-two (two equations, two variables) system. It's easiest by substitution.

`H + 3H = 464`

`4H = 464`

`H = 116`

So, we sold 116 history books. We put our known number back into Equation 2 at the beginning, and find out that we sold 116 * 3, or 348, physics books.

Thus, the store sold 348 physics books and 116 history books.