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Money
Jar
Answer
:
0
pennies, 3
nickels, 21
dimes, 31 quarters.
AI says
There are a total of 55 coins that total $10 in value
We know there are fewer:
* Pennies than nickels
* Nickels than dimes
* Dimes than quarters
Let's define variables for the number of each coin:
* p = number of pennies
* n = number of nickels
* d = number of dimes
* q = number of quarters
Constraints:
* p < n
* n < d
* d < q
* p + n + d + q = 55 (total number of coins)
Let's write equations for the total value:
* p pennies x 1 cent per penny = p cents
* n nickels x 5 cents per nickel = 5n cents
* d dimes x 10 cents per dime = 10d cents
* q quarters x 25 cents per quarter = 25q cents
The total value is $10 = 100 cents
Substituting in:
p + 5n + 10d + 25q = 100
Solving this:
* If q = 25, then d = 15, n = 10, p = 5
* And p + n + d + q = 5 + 10 + 15 + 25 = 55
Therefore, the number of each coin is:
* Pennies: 5
* Nickels: 10
* Dimes: 15
* Quarters: 25
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