Answer:
There are 105 pennies in the piggy bank.
There are 42 nickels in the piggy bank.
Step-by-step explanation:
there are:
p pennies in the piggy bank
n nickels in the piggy bank
Then we can define T, the total number of coins, as:
T = p + n
We know that 2/7 of the total number of coins are nickels.
This can be written as:
n = (2/7)*T = (2/7)*(n + p)
And if we remove 84 pennies, 1/3 of the remaining coins are pennies.
This can be written as:
p - 84 = (1/3)*(n + p - 84)
Then we have a system of two equations:
n = (2/7)*(n + p)
p - 84 = (1/3)*(n + p - 84)
Let's solve the system, to do it, we first need to isolate one of the variables in one of the equations.
We can isolate n in the first one, to get:
n = (2/7)*(n + p) = (2/7)*n + (2/7)*p
n - (2/7)*n = (2/7)*p
n*(5/7) = (2/7)*p
n = (7/5)*(2/7)*p = (2/5)*p
n = (2/5)*p
Now we can replace this in the other equation:
p - 84 = (1/3)*(n + p - 84)
p - 84 = (1/3)*( (2/5)*p + p - 84)
Let's solve this for p
p - 84 = (1/3)*( (7/5)*p - 84)
3*(p - 84) = (7/5)*p - 84
3p - 252 = (7/5)*p - 84
3*p - (7/5)*p = 252 - 84
(15/5)*p - (7/5)*p = 168
(8/5)*p = 168
p = (5/8)*168 = 105
There are 105 pennies in the piggy bank.
And we know that:
n = (2/5)*p = (2/5)*105 = 42
There are 42 nickels in the piggy bank.
