Final answer:
To find the total capacity of Elsa's penny bank, we determined that the addition of 520 pennies accounted for 2/3 of the bank's capacity. Solving the equation 520 = 2/3 × C gave us the total capacity, which is 780 pennies.
Step-by-step explanation:
The question is about determining the total capacity of Elsa's penny bank given that it was 1/3 full and became 5/6 full after adding 520 pennies. To solve this, we use the concept of fractions and linear equations. Initially, we can denote the total capacity of the bank as 'C'. We know that after adding 520 pennies, the bank went from 1/3 of its capacity to 5/6 of its capacity, which means 520 pennies are equivalent to 5/6 - 1/3 of the capacity.
Let us calculate the fraction of the capacity that 520 pennies represent:
- 5/6 - 1/3 = (5×2 - 1×2)/(6×2) = (10 - 2)/12 = 8/12 = 2/3
So, 520 pennies are 2/3 of the total capacity C. Now we can set up an equation:
To find the total capacity, C, we divide both sides of the equation by 2/3:
- C = 520 / (2/3) = 520 × (3/2) = 780
This tells us that Elsa's bank can hold a total of 780 pennies when full.