The number of pennies ari has 14 pennies and the equation used is p+n=22 and 0.05n+0.01p=0.54
Given that ari has a total of 22 coins consisting of pennies and nickels and the total value of the coins is $0.54.
Lets assume n = the number of nickels that Ari has.
Let p = the number of pennies that Ari has.
The given total number of coins ari has is 22.
n + p = 22
So, our first equation is n+p=22.
Now, we will find our second equation
Each penny ari going to be $0.01 and a nickel is work $0.05.
And the total is $0.54
Our second equation is 0.05n + 0.01p = 0.54
Now, we will simplify first and second equation by substituting the value of p from equation (1) into equation (2).
The value of p from equation is p=22-n
Substitute value of n in equation (2), we get
0.05n+0.01(22-n)=0.54
0.05n+0.22-0.01n=0.54
0.04n+0.22=0.54
0.04n=0.54-0.22
0.04n=0.32
n=0.32/0.04
n=8
Now, substitute value of n in equation (1), we get
n+p=22
8+p=22
p=22-8
p=14
Hence, the equation used to find the number of pennies ari has when she has a total of 22 coins consisting of pennies and nickels and the total value of the coins is $0.54 is p+n=22 and 0.05n+0.01p=0.54.
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