Question 323539: Please help me solve this equation
Shane has pennies, dimes, and quarters. He has a total of $17.64. He has twice as many quarters as dimes and one-third as many dimes as pennies. How many of each coin does he have?
Answer by jessica43(140)   (Show Source):
You can put this solution on YOUR website! 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.
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