Exercise 2 Page 385

Let x be the number of binders and y be the number of calculators sold. Since the bookstore hopes to sell at least 30 of these, the sum of x and y has to be larger than or equal to 30, which we write as an inequality. x+y ≥ 30 From the table we can see that the price of a binder is $3.65 and the price of a calculator is $14.80. We can write an expression to represent how much the bookstore will get for x binders and y calculators. 3.65x+14.80yKnowing that it hopes to have sales revenue of at least $200, this expression has to be greater than or equal to 200. 3.65x+14.80y ≥ 200 Combining these two inequalities, we get a system of inequalities. x+y ≥ 30 3.65x+14.80y ≥ 200 Let's graph these inequalities to find the regions in which both of them are satisfied. To do so, we will graph the lines that limit these inequalities. We will first isolate y to find the equations of these lines.

To graph the inequalities we will start by graphing the lines y=30-x and y=13.51-0.25x. Both solution sets lie above these lines, as both inequalities describe ordered pairs with y-coordinates greater than 30-x and 13.51-0.25x. This means that we have to shade the areas above the solid lines.

The solution is the area where the shadings overlap. To find how many binders and calculators could be sold, we will check which of the given options lie in the solution set. Therefore, we will plot four points in our coordinate system. F=(25,5) &G=(12,15) H=(22,9) &J=(28,6)

Since only point H lies in the solution set, the final answer is H.