Proportions & Percentages Mastery Hub: The Industry Foundati

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Q1Domain Verified

In the context of scaling recipes, if a recipe for 4 servings requires 2 cups of flour, and you need to prepare it for 10 servings, what is the MOST efficient method to determine the required flour, considering potential waste and precision in a professional kitchen setting?

Apply a scaling factor derived from the difference in servings (10 - 4 = 6) and add this to the original amount, then adjust based on perceived ingredient density.

Calculate the ratio of new servings to old servings (10/4 = 2.5) and multiply the original flour amount by this factor (2 cups * 2.5 = 5 cups).

Use a proportion: 2 cups / 4 servings = x cups / 10 servings, and solve for x, acknowledging that this is an approximation and may require slight adjustments for practical application.

Determine the flour needed per serving (2 cups / 4 servings = 0.5 cups/serving) and then multiply by the desired number of servings (0.5 cups/serving * 10 servings = 5 cups).

Q2Domain Verified

A chef is analyzing the profit margin of two popular dishes. Dish A has a cost of goods sold (COGS) of $12 and sells for $30. Dish B has a COGS of $18 and sells for $45. If the chef wants to maintain the SAME profit margin percentage, and the COGS for Dish A increases to $15, what should the NEW selling price of Dish A be?

$37.50

$40.00

$39.00

$35.00

Q3Domain Verified

tests the understanding of profit margin percentage and its application in dynamic pricing. The profit margin percentage is calculated as ((Selling Price - COGS) / Selling Price) * 100. For Dish A, the initial profit margin is (($30 - $12) / $30) * 100 = (18/30) * 100 = 60%. For Dish B, the profit margin is (($45 - $18) / $45) * 100 = (27/45) * 100 = 60%. To maintain the 60% profit margin for Dish A with a new COGS of $15, we set up the equation: (($P_{new} - $15) / $P_{new}) = 0.60. Solving for $P_{new}$: $P_{new} - $15 = 0.60 * $P_{new}$. $P_{new} - 0.60 * $P_{new} = $15$. $0.40 * $P_{new} = $15$. $P_{new} = $15 / 0.40 = $37.50. Option A is correct. Option B is incorrect because it implies a fixed markup rather than a consistent margin percentage. Option C and D result from incorrect algebraic manipulation or miscalculation of the initial profit margin. Question: A manufacturing company uses a specific alloy composed of 60% copper and 40% zinc by weight. If the company needs to produce 500 kg of this alloy and discovers a batch of zinc is contaminated, reducing its purity by 10% (meaning only 90% of the stated weight is actual zinc), what is the MOST accurate quantity of pure copper and contaminated zinc the company must use to achieve the target 500 kg of the alloy composition?

270 kg of pure copper and 230 kg of contaminated zinc.

300 kg of pure copper and 200 kg of contaminated zinc (assuming the contaminated zinc is used at face value).

300 kg of pure copper and 222.22 kg of contaminated zin

C) 300 kg of pure copper and 180 kg of contaminated zinc.

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