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