Question

O LINEAR SYSTEMSSolving a word problem involving a sum and another basic...Michael vA textbook store sold a combined total of 260 chemistry and sociology textbooks in a week. The number of chemistry textbooks sold was three times thenumber of sociology textbooks sold. How many textbooks of each type were sold?

Answer 1

We know that:

T = total number of books = 260

C = # of chemistry books

S = # of sociology books

We also know that the number of chemistry books (C) is 3 times the number of sociology books (S):

`C=3\cdot S`

And the total number of books (T) is the sum of chemistry books (C) and sociology books (S):

`\begin{gathered} T=C+S \\ 260=C+S \end{gathered}`

We can replace the formula of chemistry books in terms of sociology books in the last equation, so:

`\begin{gathered} 260=3S+S \\ 260=4S \\ S=(260)/(4)=65 \end{gathered}`

So the number of sociology books is 65. Now, we can calculate the number of chemistry books using the first equation:

`C=3\cdot S=3\cdot65=195`

The final answer is:

C = # of chemistry books sold = 195

S = # of sociology books sold = 65