Question 1109717: You have 37 coins that are nickels, dimes, and pennies. The total value of the coins is $1.55. There are twice as many pennies as dimes. Find the number of each type of coin in the bank.
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
A purely algebraic solution to this problem would be a good exercise for learning the methods of algebra.
But this problem provides an excellent opportunity to solve the problem using logical reasoning.
Because there are twice as many pennies as dimes, the number of pennies is an even number.
And because the total value of the coins (in cents) is a multiple of 5, the number of pennies has to be a multiple of 5.
So logical analysis tells us the number of pennies must be an even multiple of 5 -- i.e., it must be a multiple of 10.
Since the total number of coins is 37, the number of pennies must then be 0, 10, 20, or 30.
Knowing that the number of dimes is half the number of pennies, and knowing the total number of coins is 37 lets you determine, for each of the possible numbers of pennies, the exact number of each type of coin. And only one of the combinations gives you a total of $1.55.
If you want to get some good, healthy mental exercise, finish solving the problem by that method....
For a traditional algebraic solution, you could do this....
let d = # of dimes
then 2d = # of pennies
Then the number of nickels is 37-d-2d = 37-3d
Now write and solve the equation that says the total value of the coins, in cents, is 155:
You can finish....
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