To determine how much sugar Joe needs if he uses 12 tablespoons of butter, we first need to establish the ratio of butter to sugar based on the original recipe.
The original recipe calls for:
- 1/4 cup of sugar
- 5 tablespoons of butter
Now, let's convert 1/4 cup of sugar to tablespoons for easier comparison. There are 16 tablespoons in a cup, so:
\[ 1/4 \text{ cup} = \frac{16 \text{ tablespoons}}{4} = 4 \text{ tablespoons} \]
So, the original recipe uses:
- 4 tablespoons of sugar
- 5 tablespoons of butter
Next, we'll find the ratio of butter to sugar:
\[ \text{Ratio of butter to sugar} = \frac{5 \text{ tablespoons of butter}}{4 \text{ tablespoons of sugar}} = \frac{5}{4} \]
Now, if Joe uses 12 tablespoons of butter, we can set up a proportion to find the amount of sugar he needs:
\[ \frac{5 \text{ tablespoons of butter}}{4 \text{ tablespoons of sugar}} = \frac{12 \text{ tablespoons of butter}}{x \text{ tablespoons of sugar}} \]
Cross-multiplying gives:
\[ 5x = 4 \times 12 \] \[ 5x = 48 \]
Now, divide both sides by 5:
\[ x = \frac{48}{5} = 9.6 \]
Thus, Joe needs 9.6 tablespoons of sugar if he uses 12 tablespoons of butter.
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