Writing systems of inequalities word problem

- [Voiceover] So we're told a cupcake requires 35 grams of sugar and 50 grams of flour. So let me underline that. "A cupcake requires 35 grams of sugar "and 50 grams of flour." And then they tell us, "A muffin requires 30 grams of sugar." So let me underline that. "A muffin requires 30 grams of sugar and 65 grams of flour." All right, so what are they going to ask us to actually do? "Shawna needs to use up at least 460 grams of sugar." So let me underline this in different color. She needs to use up, "Shawna needs to use up at least 460 grams of sugar "to make cupcakes and muffins, "and she wants to use at most 970 grams of flour." So let me use another color. "And she wants to use "at most 970 grams of flour. "Let's form a system of inequalities "to represent Shawna's conditions. "Let C denote the number of cupcakes she makes "and M the number of muffins she makes." All right, "Write an inequality that represents "the condition based on the number of grams of sugar." So the condition based on the number of grams of sugar. That's what we underlined here in green. "Shawna needs to use up at least 460 grams of sugar "to make cupcakes and muffins." So let's see how we can write that out. So how much sugar she's gonna use for the cupcakes? Well, we're told right over here she requires 35 grams of sugar per cupcake. So the amount of sugar that she's going to use for all of the cupcakes is going to be 35 grams per cupcake, let me write that a little bit neater, 35 grams per cupcake times the number of cupcakes. So this is how much sugar total she's going to use on the cupcakes. 35 grams per cupcake times the number of cupcakes. And then how many grams of sugar is she going to use for the muffins? Well, that's going to be 30 grams of sugar per muffin. So plus 30 grams of sugar per muffin times the number of muffins. So times M. So this is the total sugar from the cupcakes. This is the total sugar from the muffins. And so if you add them together, this is a total sugar that she's using and we're told that she needs to use up at least 460 grams of sugar. So everything here is in grams. So this has to be greater than or equal. She needs to use at least 460 grams of sugar to make both of these. So that's it. We can just set up the inequality that represents the condition based on the number of grams of sugar which is this condition right over here. Now let's see, this next question. Let's see, "Write an inequality that represents "the condition based on the number of grams of flour." Well, that's what we underlined in orange right over here. She needs to use no at most 970 grams of flour. So no more than 970 grams. So how would we express that as an inequality? Well, how much flour is she going to use for the cupcakes? Well, she used 50 grams of flour per cupcake. So 50 grams per cupcake times the number of cupcakes. That's how much flour she's going to use for the cupcakes. And then for the muffins, she uses 65 grams of flour per muffin times the number of muffins. So this is the total amount of flour that she is going to use and this has to be less than or equal to 970 grams. Less than or equal to 970 and we're done. And so you could actually, if you wanted to, you could say, "What pairs of C and M "satisfy both of these inequalities?" And then you could say, "Okay, that's the combination "of the number of cupcakes and muffins she can make "in order to satisfy her actual conditions."