To find the amount of brown sugar needed for 1 cup of flour, we can set up a proportion based on the given ratio.

Given:

• $\frac{3}{4}$ cup of brown sugar for 2 cups of flour.

We want to find how much brown sugar, say $x$, is needed for 1 cup of flour.

$\frac{3}{4} \text{ (cups of brown sugar)} : 2 \text{ (cups of flour)} = x : 1 \text{ (cup of flour)}$

Setting up the proportion:

$\frac{3}{4} \div 2 = x \div 1$

This simplifies to:

$x = \frac{3}{4} \times \frac{1}{2} = \frac{3}{8}$

So, Colin should use $\frac{3}{8}$ cup of brown sugar for 1 cup of flour.

Answer:

$\frac{3}{8} \text{ cup of brown sugar}$

Would you like more details or have any questions?

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1. How much brown sugar is needed for 3 cups of flour?
2. What is the ratio of flour to brown sugar in this recipe?
3. If Colin has 4 cups of flour, how much brown sugar will he need?
4. How would the proportion change if he used 1 cup of sugar for every 2 cups of flour?
5. Can we solve this using unit rates instead?

Tip: Proportions help find equivalent ratios easily by scaling quantities up or down.