Proportion word problem (example 1) | 7th grade | Khan Academy

TL;DR

Determine the amount of flour needed for a big batch of oatmeal cookies using 9 cups of oatmeal.

Transcript

A recipe for oatmeal cookies calls for 2 cups of flour for every 3 cups of oatmeal. How much flour is needed for a big batch of cookies that uses 9 cups of oatmeal? So let's think about what they're saying. They're saying 2 cups of flour. So 2 cups of flour for every 3 cups of oatmeal. And so they're saying, how much flour is needed for a big batch... Read More

Key Insights

• 💘 The recipe calls for 2 cups of flour for every 3 cups of oatmeal.
• 🪡 Using common sense, when tripling the amount of oatmeal, you need to triple the amount of flour as well.
• 😵 Setting up a proportion equation and cross-multiplying can also help find the amount of flour needed.
• ✖️ Cross-multiplication works due to algebraic principles, ensuring equality between the multiplied diagonals.
• 🥺 In this specific case, both common sense and algebra lead to the same answer of 6 cups of flour.
• 🥳 It is important to follow the given ratio of flour to oatmeal to maintain the intended taste and texture of the cookies.
• 😵 Manipulating the proportion equation with algebra allows for a deeper understanding of the mathematical reasoning behind cross-multiplication.

Questions & Answers

Q: How much flour is needed for a big batch of oatmeal cookies that uses 9 cups of oatmeal?

6 cups of flour are needed for the cookies. The recipe requires a ratio of 2 cups of flour for every 3 cups of oatmeal, so when using 9 cups of oatmeal, the flour amount should be tripled.

Q: Can I use algebra to solve this problem?

Yes, you can use algebra. By setting up a proportion equation and cross-multiplying, you can solve for the unknown quantity of cups of flour. In this case, the answer is still 6 cups of flour.

Q: Why does cross-multiplication work in this context?

Cross-multiplication works because it is based on algebraic principles. When setting up a proportion equation, multiplying the diagonals ensures that the two sides of the equation remain equal. It simplifies the equation and allows you to solve for the unknown quantity.

Q: Can I use a different ratio for the flour and oatmeal?

No, you should use the given ratio of 2 cups of flour for every 3 cups of oatmeal. Changing the ratio would alter the proportions of the recipe and potentially result in different taste and texture.

Summary & Key Takeaways

• A recipe calls for 2 cups of flour for every 3 cups of oatmeal.

• When using 9 cups of oatmeal, you would need 6 cups of flour.

• You can solve this by using common sense or setting up a proportion equation.