Question

a textbook store sold a combined total of 340 history and sociology textbooks in a week. the number of history textbooks sold was three times the number of sociology textbooks sold. how many textbooks of each type were sold?

Answer 1

85 sociology books

255 history books

Explanation:

h = history textbooks

s = sociology textbooks

h + s = 340

h = 3s

3s + s = 340

4s = 340

s = 85

h = 3s = 3(85) = 255

Answer 2

255 history textbooks

85 sociology textbooks

Explanation:

Define the variables:

• Let x be the number of history textbooks sold.
• Let y be the number of sociology textbooks sold.

Given information:

• Total number of textbooks sold in a week was 340.
• The number of history textbooks sold was three times the number of sociology textbooks sold.

Create a system of equations with the given information and defined variables:

`\begin{cases}x+y=340\\\;\;\;\:\:\:\:x=3y\end{aligned}`

Substitute the second equation into the first equation and solve for y:

`\implies 3y+y=340`

`\implies 4y=340`

`\implies y=340 / 4`

`\implies y=85`

Substitute the found value of y into the second equation and solve x:

`\implies x=3 * 85`

`\implies x=255`

Therefore, the number of each type of textbooks sold were:

• 255 history textbooks.
• 85 sociology textbooks.