Learn Before
Solving a Proportion Application: Calories in a Larger Beverage
Apply the proportion-solving strategy to determine the calorie content of a differently sized beverage.
Problem: A 16-ounce iced caramel macchiato has 230 calories. How many calories are there in a 24-ounce iced caramel macchiato?
- Identify what to find and assign a variable: How many calories are in the 24-ounce drink? Let = calories in 24 ounces.
- Translate into a proportion, keeping units consistent — calories over ounces equals calories over ounces:
- Solve by multiplying both sides by the LCD, which is :
Remove common factors on each side. On the left, , so the left side becomes . On the right, , so the right side becomes :
Divide both sides by :
- Check reasonableness: 345 calories for a 24-ounce drink is more than 230 calories for a 16-ounce drink, but not excessively so — this is consistent with a proportional increase in size.
- Verify by substituting back into the original proportion:
✓
Answer: There are 345 calories in a 24-ounce iced caramel macchiato.
Like the medication dosage problem, this example reinforces the importance of setting up the proportion with matching units on each side (calories over ounces). The LCD of 48 is found from the denominators 16 and 24, and after clearing fractions the equation reduces to a straightforward division.
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Learn After
A health coordinator is using a proportion to calculate the calories in a 24-ounce smoothie based on a 12-ounce version. According to the standard proportion-solving strategy, which rule should be followed when 'translating' this scenario into an equation?
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A food services manager is developing a training manual for calculating nutritional data across different serving sizes. Match each step of the standard proportion-solving strategy with the specific action that must be taken when determining the calories in a larger beverage.
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A food service manager is using the standard five-step strategy to calculate calories for a larger beverage size. True or False: The 'Check Reasonableness' step involves substituting the calculated value back into the original proportion to ensure the mathematical accuracy of the solution.
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A nutrition consultant is following the standard 5-step strategy to calculate the calorie content for a new 24-ounce beverage size based on a 16-ounce version. During the 'Solve' step, the consultant clears the fractions from the proportion by multiplying both sides of the equation by the ____.
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