Let
x---------> the total number of coins
we know that
512 cents-------> is equal to $5.12
1 penny is equal to $0.01
1 nickel is equal to 5 penny--------> $0.05
1 dime is equal to 2 nickel--------> $0.10
[tex]\frac{x}{3}*0.01+ \frac{x}{3}*0.05+\frac{x}{3}*0.10=5.12[/tex]
[tex]\frac{x}{3}*[0.01+0.05+0.1]=5.12 \\\\x*[0.16]=15.36 \\\\ x=\frac{15.36}{0.16} \\\\x= 96\ coins[/tex]
the total number of coins are 96
Divide 96 by 3 to obtain the number of coins of each type
therefore
the answer is
the number of penny coins are [tex]32[/tex]
the number of nickel coins are [tex]32[/tex]
the number of dimes coins are [tex]32[/tex]
