Question 244834
Let 


p = # of pennies,
n = # of nickels
d = # of dimes
q = # of quarters



Since "There are 40 coins in all", this means that {{{p+n+d+q=40}}} (ie add up the individual coin counts to get the total). This is your first equation.


Because "The number of nickels is twice the number of quarters", we know that {{{n=2q}}}


Since "The number of quarters is two less than the number of dimes", we also know that {{{q=d-2}}}


Finally, because "A person has quarters, dimes, nickels,and pennies with a total value of $3.86", we get the equation {{{0.01p+0.05n+0.10d+0.25q=3.86}}}


Remember that a penny is $0.01, a nickel is $0.05, a dime is $0.10, and a quarter is $0.25. If you multiply those individual values by their counts (the defined variables) and add them all up, you'll get the total coin value $3.86



So the fourth and final equation is {{{0.01p+0.05n+0.10d+0.25q=3.86}}}



At the end of the translations, you get the four equations



{{{system(p+n+d+q=40,n=2q,q=d-2,0.01p+0.05n+0.10d+0.25q=3.86)}}}



From here, all you need to do is solve the system. There are plenty of options available, but I recommend using a calculator to set up a matrix to solve this problem.