Writing systems of inequalities word problem | Mathematics I | High School Math | Khan Academy

TL;DR

Learn how to set up inequalities to represent the conditions of using a certain amount of sugar and flour in baking cupcakes and muffins.

Transcript

• [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 t... Read More

Key Insights

• 🧁 Cupcakes require 35 grams of sugar and 50 grams of flour, while muffins require 30 grams of sugar and 65 grams of flour.
• 😫 Inequalities can be set up to represent the conditions of sugar and flour usage in baking.
• 🤶 The condition of using at least 460 grams of sugar can be represented as 35C + 30M ≥ 460.
• 😀 The condition of using at most 970 grams of flour can be represented as 50C + 65M ≤ 970.
• 🧁 Finding pairs of cupcakes and muffins that satisfy both inequalities can determine the number of each item Shawna can make.
• 😫 This analysis provides an understanding of how to set up inequalities for baking calculations.
• ❓ The given content focuses on mathematical problem-solving in the context of a baking scenario.
• 😫 By setting up the inequalities, Shawna can plan her baking quantities to meet the required sugar and flour limits.

Questions & Answers

Q: How can we represent the condition based on the number of grams of sugar in an inequality?

The condition is Shawna needing to use at least 460 grams of sugar. This can be represented as 35C + 30M ≥ 460, where C represents the number of cupcakes and M represents the number of muffins.

Q: How can we represent the condition based on the number of grams of flour in an inequality?

The condition is Shawna needing to use at most 970 grams of flour. This can be represented as 50C + 65M ≤ 970, where C represents the number of cupcakes and M represents the number of muffins.

Q: What pairs of C and M satisfy both inequalities?

Pairs of C and M that satisfy both inequalities represent the number of cupcakes and muffins Shawna can make to meet the given conditions.

Summary & Key Takeaways

• To make cupcakes, 35 grams of sugar per cupcake and 50 grams of flour per cupcake are required.

• Muffins require 30 grams of sugar per muffin and 65 grams of flour per muffin.

• Inequalities can be set up to represent the conditions of using at least 460 grams of sugar and at most 970 grams of flour.