Final answer:
The baker made 15 batches of cupcakes by using the total amount of sugar (4 2/7 bags) and dividing it by the amount used per batch (2/7 bag).
Step-by-step explanation:
The student asked how many batches of cupcakes a baker made if the baker uses 2/7 of a bag of sugar for every batch and used 4 2/7 bags of sugar in total.
To solve this, we convert the mixed number 4 2/7 to an improper fraction which gives us 30/7.
Then, we divide the total amount of sugar used by the fraction of sugar used per batch:
\(\frac{30}{7} \div \frac{2}{7} = \frac{30}{7} \times \frac{7}{2} = 15\)
Therefore, the baker made 15 batches of cupcakes.