A boy has twice as many nickels as he has pennies, and he has 5 less dimes than nickels. If he has $4.46 in all, how many coins of each kind does he have?

N=2p

n/2=p

n-5=d

10d+5n+1p=446

subsitute n/2 for p

subsitute n-5 for d

10 (n-5) + 5n+n/2=446

times 2 both sides

20 (n-5) + 10n+n=892

expand

20n-100+10n+n=892

31n-100=892

add 100 both sides

31n=992

divide both sides by 31

n=32

subsitute back

n/2=p

32/2=16=p

n-5=d

32-5=d=27

27 dimes

16 pennies

32 nickles