Miguel has one dollar in change. he has twice as many nickels as dimes. he has 14 more pennies than quarters. what coins does he have?

D=dimes
n=niclkes
p=pennies
q=quarters

1 dollar (100 cents)
2 times as many nickles as dimes
n=2d

14 more pennies than quarters
p+14=q

and total is 1 dollar so
25q+10d+5n+p=100
ok so we must use logic
the max number of quarters in a dolar is 4
but there are pennies so max is 3
so q=1,2, or 3
therefor p=15,16 or, 17

also, the rest of te coins are only multipules of 5 so the sum amount of pennies and quartes must add to a multiplule of 5

if q=1 and p=15, total is 40 cents
if q=2 and p=16, total is 66 cents
if q=3 and p=17, total is 92 cents
only 40 cents is a multiplule of 10

1 quarter and 15 pennies
now we are having
40 cents is pennies and quartesrs
therfor 100-40=60 cents is nickles and dimes
60=5n+10d
n=2d
sub
60=5(2d)+10d
60=10d+10d
60=20d
divide both sides by 20
3=d
sub
n=2d
n=2(3)
n=6

6 nickles
3 dimes

answer is
1 quarter
3 dimes
6 nickles
15 pennies