A textbook store sold a combined total of 240 math and history textbooks. The number of history textbooks sold was 72 less than the number of math. How many of each type of textbooks was sold.

Question

A textbook store sold a combined total of 240 math and history textbooks in a week. The number of history textbooks in 72 less than the number of math textbooks sold. How many textbooks of each type was sold.

Answer 1

We have two types of textbooks. Let's use "x" to represent the number of math textbooks and "y" to represent the number of history textbooks.

Altogether, the bookseller sold 240 math and history textbooks. So:

x + y = 240

Now, the number of history textbooks sold was 72 less than the number of math books sold. So:

y = x - 72

Now we can substitute for y in the equation and solve:

x + y = 240

x + (x - 72) = 240

2x - 72 = 240

2x = 312

x = 156

The bookseller sold 156 math textbooks.

Since y = x - 72, he must have sold 84 history textbooks.

Let's check our answers:

x + y = 240

156 + 84 = 240

That is true, so we did get the correct answers.

Answer 2

You need to set up two equations. The first will be math + history = 240, or m + h = 240.

The second shows the relationship between the two types of books: h = m - 72

Since you can't solve an equation with two variables, use the second equation to replace the "h" in the first equation: m + m - 72 = 240.

Now solve for m: 2m - 72 = 240

Add 72 to both sides: 2m = 312

Divide both sides by 2: m = 156

So 156 math textbooks were sold. Now plug that into the first equation for "m": 156 + h = 240

Subtract 156 from both sides: h = 84

So 84 history textbooks were sold.