6) Samantha likes to bake. She knows that her cookie recipe calls for 3 cups of sugar, 2 eggs, and 4 teaspoons of butter. How much sugar will she need if she uses 22 teaspoons of butter?

To find out how much sugar Samantha will need if she uses 22 teaspoons of butter, we can set up a proportion based on the ratio of butter to sugar in the recipe. Given: - 4 teaspoons of butter corresponds to 3 cups of sugar We can set up the proportion as follows: \[ \frac{4 \text{ teaspoons of butter}}{3 \text{ cups of sugar}} = \frac{22 \text{ teaspoons of butter}}{x \text{ cups of sugar}} \] Where \( x \) represents the amount of sugar needed when using 22 teaspoons of butter. Now, we can solve for \( x \) by cross-multiplying and then dividing to find the value of \( x \). Solve the equation by following steps: - step0: Solve for \(x\): \(\frac{4}{3}=\frac{22}{x}\) - step1: Find the domain: \(\frac{4}{3}=\frac{22}{x},x\neq 0\) - step2: Swap the sides: \(\frac{22}{x}=\frac{4}{3}\) - step3: Rewrite the expression: \(x=\frac{22\times 3}{4}\) - step4: Divide the terms: \(x=\frac{33}{2}\) - step5: Check if the solution is in the defined range: \(x=\frac{33}{2},x\neq 0\) - step6: Find the intersection: \(x=\frac{33}{2}\) Samantha will need 16.5 cups of sugar if she uses 22 teaspoons of butter in her cookie recipe.