Question

A baker is making sugar cookies for a local bakery. For one large batch of cookies, she needs 6 eggs and 4 cups of sugar.

1. Write a ratio statement to represent the eggs and sugar needed for 1 batch.
2. How much of each ingredient does she need for 5 batches? Write an equivalent ratio to represent this situation.
3. How much of each ingredient does she need for ½ of a batch? Write an equivalent ratio to represent this situation.
4. How much of each ingredient does she need for ¼ of a batch? Write an equivalent ratio to represent this situation.

Answer 1

To calculate the ingredients needed for different batch sizes, we scale the original ratio of eggs to sugar, which is 6:4 (simplified to 3:2). Multiplying these amounts by the desired batch size, we can obtain the quantities needed for 5 batches, ½ batch, and ¼ batch. These calculations are based on a simple scaling of the original ratio.

Step-by-step explanation:

To solve this problem, we need to understand ratios and how to scale them for different amounts of ingredients in recipes.

1. The ratio of eggs to sugar for 1 batch of cookies is 6 eggs to 4 cups of sugar, which can also be written as 6:4 or 3:2 after simplifying.
2. For 5 batches, the baker would need 5 times the original amount of each ingredient. So, she would need 6 eggs × 5 = 30 eggs and 4 cups of sugar × 5 = 20 cups of sugar. Thus, the ratio for 5 batches is 30 eggs to 20 cups of sugar (30:20 or 3:2 when simplified).
3. For ½ of a batch, the baker would need ½ times the original amount. So, she would need 6 eggs × ½ = 3 eggs and 4 cups of sugar × ½ = 2 cups of sugar. The ratio for ½ a batch is 3 eggs to 2 cups of sugar (3:2).
4. For ¼ of a batch, the baker would need ¼ times the amount. So, she would need 6 eggs × ¼ = 1.5 eggs and 4 cups of sugar × ¼ = 1 cup of sugar. The ratio for ¼ a batch is 1.5 eggs to 1 cup of sugar (1.5:1).