To solve this system let
q = number of quarters
d = number of dimes
n = number of nickels
p = number of pennies.
Since the total amount of money (in pennies) is 154 we have
25 q + 10 d + 5 n + p = 154
We also have d = 2 q ; n = 3 d ; d = p
These last three equations can be rearranged to :
q = p/2 ; n = 3 p ; d = p These can then be substituted into the first equation to get
25 (p/2) + 10 p + 15 p + p = 154 A factor of p can be taken out of the left side to get
[25/2 +10 + 15 + 1] p = (77/2) p = 154 and so
p = 4
From there we can work back to get d = 4 ; n = 12 ; q =2. This does check out.