Mrs tan baked some muffins and packed them i big and small boxes for sale.Each big bbox contained 4 muffins and each small box contained 2 muffins.At first,there were 4 times as many small boxes as big boxes.After she had sold half of the small boxes and some big boxes,she baked some more muffins and packed them into 5 big boxes.How many big boxes of muffins did she sell if she had 360 muffins left?
To solve this problem, we can break it down into steps:
Step 1: Let's assume the number of big boxes Mrs Tan had at first was x. Since there were 4 times as many small boxes as big boxes, the number of small boxes at first would be 4x.
Step 2: Each big box contained 4 muffins, so the total number of muffins in the big boxes at first would be 4x * 4 = 16x.
Step 3: Each small box contained 2 muffins, so the total number of muffins in the small boxes at first would be 4x * 2 = 8x.
Step 4: The total number of muffins Mrs Tan had at first would be the sum of the muffins in the big and small boxes: 16x + 8x = 24x.
Step 5: After selling half of the small boxes, Mrs Tan would have 4x/2 = 2x small boxes remaining. This means the total number of muffins in the remaining small boxes is 2x * 2 = 4x.
Step 6: Mrs Tan baked some more muffins and packed them into 5 big boxes, which means she added 5 * 4 = 20 muffins.
Step 7: The total number of muffins Mrs Tan had after baking more is 24x + 20.
Step 8: We are given that Mrs Tan had 360 muffins left, so we can set up an equation: 24x + 20 = 360.
Step 9: Solve the equation for x: 24x = 360 - 20 = 340. Dividing both sides by 24, we have x = 340/24 = 14.16.
Since the number of boxes cannot be a fraction, we can round down to the nearest whole number. Therefore, Mrs Tan had 14 big boxes at first.
Answer: Mrs Tan sold 14 big boxes of muffins.