Question

A cupcake recipe requires 35 grams of sugar and 50 grams of flour. A muffin recipe requires 30 grams of sugar and 65 grams of flour. Imani needs to use at least 460 grams of sugar to make cupcakes and muffins, and she wants to use at most 970 grams of flour. Which of the following systems of inequalities represents this situation in terms of? C and M, where C is the number of cupcakes she makes, and M is the number of muffins she makes. (A) 35C + 30M < 460 50C + 65M >970 (B) 35C + 30M > 460 500 + 65M < 970 (C) 30C + 35M > 460 65C + 50M < 970 (D) 30C + 35M < 460 65C + 50M > 970

Answer 1

We wre told that a cupcake recipe requires 35 grams of sugar and 50 grams of flour. A muffin recipe requires 30 grams of sugar and 65 grams of flour.

The total amount of sugar to be used for both cupcakes and muffins is at least 460 grams. This means that it must be greater than or equal to 460

If C represents cupcakes, the portion of sugar that would be used for the cupcake is 35C

If M represents muffins, the portion of sugar that would be used for the muffin is 30M

Thus, the inequality for the amount of sugar used is

`35C\text{ + 30M }\ge\text{ 460}`

The total amount of flour to be used for both cupcakes and muffins is at most 970 grams. This means that it must be less than or equal to 970

If C represents cupcakes, the portion of flour that would be used for the cupcake is 50 C

If M represents muffins, the portion of flour that would be used for the muffin is 65M

Thus, the inequality for the amount of flour used is

`\begin{gathered} 50C\text{ + 65M }\leq970 \\ \text{Thus, the required inequality is} \\ 35C\text{ + 30M }\ge\text{ 460} \\ 50C\text{ + 65M }\leq\text{ 970} \end{gathered}`