To find out how much sugar is needed when using 12 tablespoons of butter, we first need to determine the ratio of butter to sugar in the original recipe.
The original recipe calls for:
- 1/4 cup of sugar
- 5 tablespoons of butter
Now, let's convert the sugar to tablespoons for easier comparison. There are 16 tablespoons in 1 cup, so:
\[ \frac{1}{4} \text{ cup} = \frac{1}{4} \times 16 \text{ tablespoons} = 4 \text{ tablespoons of sugar} \]
Now, we have:
- 4 tablespoons of sugar
- 5 tablespoons of butter
Next, we find the ratio of sugar to butter:
\[ \text{Ratio of sugar to butter} = \frac{4 \text{ tablespoons of sugar}}{5 \text{ tablespoons of butter}} \]
Now, we need to scale this up to 12 tablespoons of butter. We set up a proportion to find the amount of sugar needed:
\[ \frac{4 \text{ tablespoons of sugar}}{5 \text{ tablespoons of butter}} = \frac{x \text{ tablespoons of sugar}}{12 \text{ tablespoons of butter}} \]
Now, cross-multiply to solve for \( x \):
\[ 4 \times 12 = 5 \times x \]
\[ 48 = 5x \]
Now divide by 5:
\[ x = \frac{48}{5} = 9.6 \text{ tablespoons of sugar} \]
Therefore, if he uses 12 tablespoons of butter, he will need 9.6 tablespoons of sugar.
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