A chef uses a recipe with the following ingredients. Then the chef decides to make more than 1 batch of the recipe.
| Fruit | Cups Used |
| ----------- | --------- |
| Apples | 5 |
| Mangoes | 3 |
| Blueberries | 2 |
| Blackberries | 1 |
If a total of 30 cups of mangoes and blueberries are used, how many batches of the recipe did the chef make?
A. 4 batches
B. 5 batches
C. 6 batches
D. 7 batches
Answer (1)
• Define 'b' as the number of batches. • Express the total cups of mangoes and blueberries as 3 b + 2 b = 30 .
• Simplify the equation to 5 b = 30 .
• Solve for b to find the number of batches: 6 .
Explanation
Understanding the Problem Let's analyze the problem. We know the recipe uses 3 cups of mangoes and 2 cups of blueberries per batch. The chef made multiple batches, and in total, 30 cups of mangoes and blueberries were used. We need to find the number of batches the chef made.
Setting up the Equation Let 'b' represent the number of batches the chef made. The total amount of mangoes used is 3b cups, and the total amount of blueberries used is 2b cups. The sum of mangoes and blueberries is 3b + 2b, which equals 30.
Formulating the Equation Now, we set up the equation: 3 b + 2 b = 30
Simplifying the Equation Combine the like terms: 5 b = 30
Solving for b To solve for 'b', divide both sides of the equation by 5: b = 5 30 The result of the operation is 6.
Final Answer Therefore, the chef made 6 batches of the recipe.
Examples
Understanding how to scale recipes is a practical skill in cooking and baking. For example, if you want to bake a cake for a larger group of people than the recipe originally serves, you need to multiply all the ingredients by the same factor. If the original recipe uses 2 cups of flour and you want to triple the recipe, you would need 6 cups of flour. This ensures that the ratios of ingredients remain the same, and the cake turns out as expected. Scaling recipes accurately is essential for consistent and delicious results.
