Linear inequality

Question

Suppose you are shopping for notebooks and pad papers for a fund drive. Notebook (x) costs 15 and paper (y) costs 12. You have at most 1500 to spend.

1. Write a linear inequality in two variables that will describe the situation:

2. At most how many notebooks can be bought if 100 pad papers were already purchased?

3. Is it possible to buy 70 notebooks and 40 pad papers? Why do you say so?

Answer 1

1. 15X+12Y ≤ 1500
2. If Y=100, then 15X +12*100 = 15X + 1200 ≤ 1500. This means 15X ≤ 300 or X ≤ 20. At most 20 notebooks may be purchased.
3. No, because: 15*70 + 12*40 = 1530 which is exceeds total budget of 1500.