Final answer:
To determine the capacity of Ivanna's penny bank, we calculate the difference in fractions to equate to the number of pennies added. We find that the penny bank can hold a total of 960 pennies.
Step-by-step explanation:
Understanding Penny Bank Capacity through Fractions
Ivanna's penny bank was 1/6 full, and after adding 320 pennies, it became 1/2 full. To find out the total capacity of the bank, we can set up a proportion since the number of pennies added is proportional to the increase in the bank's capacity.
Let's denote the total capacity of the bank as C. Initially, the bank has C/6 pennies, and after adding 320 pennies, it has C/2 pennies. The difference between C/2 and C/6 is 320 pennies.
We can set up the following equation: C/2 - C/6 = 320
To solve this equation, find a common denominator, which is 6 in this case, and subtract C/6 from C/2 which can be rewritten as 3C/6 to obtain:
(3C/6 - C/6) = 320
This simplifies to:
(2C/6) = 320
Multiply both sides by 6/2 to solve for C:
C = 320 × (6/2)
C = 960
Therefore, Ivanna's penny bank can hold a total of 960 pennies.