Final answer:
To find the total capacity of Lena's penny bank, we determine that adding 280 pennies fills up half of the bank's capacity. From this, we conclude that if 280 pennies fill half the bank's capacity, then the total capacity is 560 pennies.
Step-by-step explanation:
The student is asking how many pennies Lena's bank can hold. Lena's bank is initially 1/6 full, and after adding 280 pennies, it becomes 2/3 full.
Firstly, we recognize that 2/3 is equivalent to 4/6. This means that Lena adding 280 pennies resulted in an increase of 4/6 - 1/6 = 3/6 (or 1/2) of the bank's capacity. Thus, 280 pennies equal half the bank's capacity. To find the full capacity, we multiply 280 by 2, which gives us 560 pennies. Therefore, Lena's bank can hold 560 pennies in total.