It takes

Question

\[40\] ink cartridges and
\[200\] pages to print a book, and it takes
\[30\] ink cartridges and
\[80\] pages to print a magazine.
Sarah wants to print books and magazines with at most
\[300\] ink cartridges and
\[1200\] pages.
Let
\[B\] denote the number of books she prints and
\[M\] the number of magazines she prints.
Write an inequality that represents the condition based on the number of ink cartridges.
Write an inequality that represents the condition based on the number of pages.

Answer 1

To express the conditions based on the number of ink cartridges and pages for Sarah's printing of books and magazines, we can write the inequalities as follows:

1. Ink Cartridges Inequality: Since each book requires 40 ink cartridges and each magazine requires 30 ink cartridges, the total number of ink cartridges used cannot exceed 300. This can be expressed as: \[ 40B + 30M \leq 300 \]

2. Pages Inequality: Since each book requires 200 pages and each magazine requires 80 pages, the total number of pages used cannot exceed 1200. This can be expressed as: \[ 200B + 80M \leq 1200 \]

Thus, the two inequalities that represent the conditions are:

1. \( 40B + 30M \leq 300 \)
2. \( 200B + 80M \leq 1200 \)