Writing systems of inequalities word problem

so we're told a cupcake requires 35 grams of sugar and 50 grams of flowers let me let me underline that so a cupcake requires 35 grams of sugar and 50 grams of flour and then they tell us 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 sugars let me underline this in a 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 do this in 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's see 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 is she going to use for the cupcakes well we're told 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 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 30 grams of sugar per muffin times the number of muffins so times em so this is a 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 is this has to be greater than or equal she has to use at least 460 grams of sugar to make both of these so that's it we have 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 they say writing in write and inequality that represents the condition based on the number of grams of flour well that's what we underlined an 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 flours you're going to use for the cupcakes well she use 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 a total amount of flour that she's 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 well what what comment what pairs of C and M satisfy both of these inequalities and then you can say okay that's a combination of the number of cupcakes and muffins she could you make in order to satisfy her actual conditions