We are given
piggy bank has nickels , dimes and quarters
Let's assume
number of nickels =n
every two nickels there are 3 dimes
so, number of dimes are
[tex]=\frac{3}{2}n[/tex]
[tex]=1.5n[/tex]
every two dimes that are 5 quarters there
so, number of quarters are
[tex]=\frac{5}{2}\times 1.5n[/tex]
[tex]=3.75n[/tex]
so, total number of coins = number of nickels + number of dimes +number of quarters
total number of coins =n+1.5n+3.75
there are 500 coins
so, we get
[tex]n+1.5n+3.75n=500[/tex]
now, we can solve for n
[tex]6.25n=500[/tex]
divide both sides by 6.25
so, we get
[tex]n=80[/tex]
number of dimes is 1.5n
[tex]=1.5\times 80[/tex]
[tex]=120[/tex]
number of quarters is 3.75n
[tex]=3.75\times 80[/tex]
[tex]=300[/tex]
so,
Number of nickels =80
Number of dimes =120
Number of quarters =300............Answer
