Beth wants to make exactly 60 blueberry muffins. Each batch makes 6 muffins. She has already made 2.5 batches. How many more batches of blueberry muffins does Beth need to make?
The Correct Answer and Explanation is:
Answer: 7.5 more batches
Beth’s baking plan can be broken into three clear arithmetic steps:
- Translate batches into actual muffins already produced. A single batch yields 6 muffins. Beth has already completed 2.5 batches, so the number of finished muffins is 6 muffins × 2.5 batches = 15 muffins.
- Work out how many muffins are still required to hit the target of 60. Subtract the muffins already on hand from the desired total: 60 – 15 = 45. Beth therefore still needs 45 muffins.
- Convert the remaining muffin requirement back into batches. Because each fresh batch will again turn out 6 muffins, divide the needed muffins by the batch size: 45 ÷ 6 = 7.5.
The quotient 7.5 tells us that seven full batches would be insufficient (7 × 6 = 42 muffins, leaving a 3-muffin shortfall), while eight full batches would overshoot (8 × 6 = 48 muffins, producing an unwanted surplus of 3). Since Beth has already demonstrated she can handle half-batches—she made half a batch earlier—she can simply repeat that approach: make seven complete batches and finish with one half batch. That produces exactly the 45 additional muffins she needs (7 × 6 + 0.5 × 6 = 42 + 3 = 45), bringing the running total to the desired 60.
In more general terms, the formula behind the calculation is
additional batches = (target muffins – completed batches × muffins per batch) ÷ muffins per batch.
Plugging in Beth’s numbers yields (60 – 2.5 × 6) ÷ 6 = 45 ÷ 6 = 7.5.
Thus, Beth must bake 7.5 more batches to meet her goal precisely, without waste or shortage. Simple ratios keep bakers on target, preventing any surplus or disappointing shortages in practice. Mastering such proportional reasoning is essential for scaling recipes confidently and efficiently today.
