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To solve this problem you are going to write three equations using the given information.
First,you know that the total value of Shane's money is $17.64 and the value of a penny is $0.01, a dime is $0.10 and a quarter is $0.25:
0.01(P) + 0.10(D) + 0.25(Q) = 17.64 (P = number of pennies, D= number of dimes, Q= number of quarters)
Second, you know that Shane has twice as many quarters as dimes:
Q = 2(D)
Finally, you know that he has one-third as many dimes as pennies:
D = (1/3)P
You can also rewrite this as P = 3(D)
Now to solve this problem you want to plug in the second and third equations into the first equation. Since the variable D is found in all three equations, we want that to be the remaining variable we solve for. That means, plug in the other equations to replace the Q and the P:
0.01(P) + 0.10(D) + 0.25(Q) = 17.64
0.01(3D) + 0.10(D) + 0.25(2D) = 17.64
0.03D + 0.10D + 0.5D = 17.64
0.63D = 17.64
D = 28
Now plug in this value into the first equation to solve for Q:
Q = 2D
Q = 2(28)
Q = 56
Now plug in this value into the second equation to solve for P:
P = 3D
P = 3(28)
P = 84
So Shane has 28 dimes, 56 quarters and 84 pennies.