The inequality that represents the condition based on the number of grams of sugar is 35C + 30M ≥ 460
The  inequality that represents the condition based on the number of grams of flour is 50C + 65M ≤ 970
Solution:
Given, a cupcake requires 35 grams of sugar and 50 grams of flour, and a muffin requires 30 grams of sugar and 65 grams of flour. Â
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.
Let C denote the number of cupcakes she makes and M the number of muffins she makes. Â
Now, let us write an inequality that represents the condition based on the number of grams of sugar. Â
Total sugar used ≥ 460 grams.
Sugar used for cupcakes + sugar used for muffins ≥ 460 grams
Number of cupcakes x sugar used for 1 cupcake + number of muffins x sugar for 1 muffin ≥ 460
C [tex]\times[/tex] 35 + M [tex]\times[/tex] 30 ≥ 460
35C + 30M ≥ 460
Now let us write an inequality that represents the condition based on the number of grams of flour.
Total flour used ≤ 970 grams.
Flour used for cupcakes + flour used for muffins ≤ 970 grams
Number of cupcakes x flour used for 1 cupcake + number of muffins x flour for 1 muffin ≤ 970
C [tex]\times[/tex] 50 + M [tex]\times[/tex] 65  ≤ 970.
50C + 65M ≤ 970
Hence, the inequalities are 35C + 30M ≥ 460 and 50C + 65M ≤ 970.
Answer:
35C+30M[tex]\geq[/tex]460
50C+65M[tex]\leq[/tex]970
Step-by-step explanation:
