Answer:
Explanation:
w = number of pennies
x = number of nickels
y = number of dimes
z = number of quarters
0.01w + 0.05x + 0.10y + 0.25z = $104
w + x + y + z = 1000
w = 4x
w = 2y
nickels, dimes and pennies are in a ratio of 1:2:4
if there is 1 nickel, the value of penny + nickel + dime is $0.29
As we know the sum of all the coins is a whole dollar, we must find a point where multiples of 0.29 end in .00, 0.25, 0.50 or 0.75 so that quarters can make up the difference.
This first occurs at a count of 25 nickels, 50 dimes and 100 pennies.
That is 175 coins summing a total of $7.25
1000 coins / 175 coins/set = 5.71... sets
We know that we can only use full sets to reach an even dollar amount.
We only have a potential 5 sets to check, but because our set value comes to $7.25, let's guess at 4 sets to make the decimal portion go to .00
4($7.25) = $29
$104 - $29 = $75
$75 in quarters is 75(4) = 300 coins
300 + 4(175) = 1000 coins BINGO
4(1)(25) = 100 nickels
4(2)(25) = 200 dimes
4(4)(25) = 400 pennies
300 quarters
