Question 908946: Please help me solve this word problem: A bag contains twice as many pennies as nickels and four more dimes than quarters. Find all possibilities for the number of each coin if their total value is $2.01
Answer by JulietG(1812)   (Show Source):
You can put this solution on YOUR website! First, we know it must contain at least one penny. Since it contains twice as many pennies as nickels, it either contains no nickels, or at least six pennies.
How we can make it with one penny and no nickels? Can we, given the restriction that it has four more dimes than quarters.
Assuming we're looking for $2.00 with just quarters and dimes.
The possibilities are 2 quarters and 15 dimes, 4 quarters and 10 dimes, 6 quarters and 5 dimes, or 8 quarters.
None of those fits the parameters. So a single penny is out of the equation.
How about 6 pennies? It would then need to contain 3 nickels. The resulting amount is $1.80. How do we make that with quarters and dimes?
2 quarters and 13 dimes, 4 quarters and 8 dimes, 6 quarters and 3 dimes.
Hooray! We found one - 4 quarters, 8 dimes, 3 nickels, 6 pennies.
We can't use 11 pennies because we can't halve the nickel. 16 pennies would mean 8 nickels. That leaves $1.45.
Possible combinations of quarters and dimes are 1 quarter and 12 dimes, 3 quarters and 7 dimes, 5 quarters and 2 dimes.
Looks like we found another! 3 quarters, 7 dimes, 8 nickels, 16 pennies.
We can't use 21 pennies. How about 26?
26 pennies and 13 nickels is .86, leaving $1.15 for the Q/D.
1 quarter and 9 dimes, 3 quarters and 4 dimes. None fit.
No dice on 31 pennies. What about 36?
36 pennies and 18 nickels = $1.26, leaving 75 for the Q/D.
1 quarter and 5 dimes, or 3 quarters. Nothing here either.
46 pennies and 23 nickels = $1.61, leaving .40 for the Q/D
4 dimes.
Beyond that, there are no Q/D possibilities, and I didn't come up with a P/N equation.
I'm just finding the two possibilities. Do you see more?
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