Final answer:
Clayton can make 5 batches of mixed-berry muffins with the berries he picked, as he has a total of 15/4 cups of berries and each batch requires 3/4 cup of berries.
Step-by-step explanation:
The question asks how many batches of mixed-berry muffins Clayton can make with the berries he picked if each batch requires ¾ cup of berries. Clayton picks 1 ¼ cups of blackberries and twice as many raspberries, which equals 2 × 1 ¼ cups = 2 × 5/4 cups = 5/2 cups of raspberries. To find the total number of cups of berries, add the blackberries and raspberries together: 1 ¼ cups + 2 ½ cups = 5/4 cups + 5/2 cups = 5/4 cups + 10/4 cups = 15/4 cups. To determine how many batches of muffins he can make, divide the total number of cups of berries by the cups needed per batch: (15/4 cups) ÷ (3/4 cups per batch) = (15/4) × (4/3) = 5 batches. Therefore, Clayton can make 5 batches of mixed-berry muffins.