A recipe for soup calls for 2 tablespoons of lemon juice and \( \frac{1}{2} \) cup of olive oil. The given recipe serves 3 people, but a cook wants to make a larger batch that serves 90 . a) How many cups of lemon juice will the chef need for the larger batch? b) How many pints of olive oil will the chef need for the larger batch? a) The chef needed \( \square \) cups of lemon juice for the larger batch. (Type a whole number, proper fraction, or a mixed number.) b) The chef needed \( \square \) pints of olive oil for the larger batch. (Type a whole number, proper fraction, or a mixed number.)

To find out how much lemon juice and olive oil the chef needs for a larger batch serving 90 people, we first need to determine the scaling factor from the original recipe. 1. The original recipe serves 3 people, so to find the scaling factor for 90 servings, we calculate: \[ \text{Scaling factor} = \frac{90}{3} = 30 \] 2. Next, let's calculate how many cups of lemon juice the chef will need for the larger batch. The recipe calls for 2 tablespoons of lemon juice for 3 servings: \[ \text{Lemon juice for 90 servings} = 2 \text{ tablespoons} \times 30 = 60 \text{ tablespoons} \] Since there are 16 tablespoons in a cup: \[ \text{Cups of lemon juice} = \frac{60}{16} = 3.75 \text{ cups} \] Thus the chef needed \( 3.75 \) cups of lemon juice for the larger batch. 3. Now for the olive oil, the recipe states \( \frac{1}{2} \) cup for 3 servings: \[ \text{Olive oil for 90 servings} = \frac{1}{2} \text{ cup} \times 30 = 15 \text{ cups} \] Since there are 2 cups in a pint: \[ \text{Pints of olive oil} = \frac{15}{2} = 7.5 \text{ pints} \] Therefore, the chef needed \( 7.5 \) pints of olive oil for the larger batch. a) The chef needed \( 3.75 \) cups of lemon juice for the larger batch. b) The chef needed \( 7.5 \) pints of olive oil for the larger batch.