Question

forrest has pennies, nickels, dimes, and quarters in a cookie jar- a total of 201 coins. He has twice as many nickels as dimes and four times as many pennies as quarters. If he has $12.10 in coins, how many of each type does he have.

Answer 1

We use letters to represent the unknown coins.
P for pennies that worth 1 cents
N for nickels that worth 5 cents
D for dimes that worth 10 cents
Q for quarters that worth 25 cents.

"He has twice as many nickels (N) as dimes (D)" So D=2N
"and four times as many pennies (P) as quarters (Q)." So Q=4P

Number of coins equals P+N+D+Q=P+N+2N+4P (Dimes and quarters are written in terms of nickels and pennies, respectively)

So, number of coins is equal to 5P+3N=201. Thats is the first equation (I)
To write the second equation, use cents of coins. 12.10 $ in coins can be shown as
 
5P. 1 cent + 3N. 5 cent=1210 cents or simply 5P + 15N=1210 (Second equation)

We have two equations and two unknowns so it is soluble.
number of coins: 5P+3N=201 (I)
cents of coins: 5P+15N=1210 (II)
Use the substitution method. (II) - (I)=12N=1009 
N=1009/12=84 ( Actually it is 84.08)
D=2N=168
P= -10
Q=-40  
Number of pennies and quarters are meaningless. They can't be negative. So they should be something wrong in the question.