Question

A cupcake requires 35 grams of sugar and 50 grams of flour, and a muffin requires 30 grams of sugar and 65

Answer 1

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.  

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.  

Now, let us write an inequality that represents the condition based on the number of grams of sugar.  

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 $\times$ 35 + M $\times$ 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 $\times$ 50 + M $\times$ 65  ≤ 970.

50C + 65M ≤ 970

Hence, the inequalities are 35C + 30M ≥ 460 and 50C + 65M ≤ 970.