You have a jar of loose change which contains pennies, nickels, dimes, and quarters. The total value of the change in the jar is $104. In total, there are exactly 1000 coins in the jar. There are four times as many pennies as there are nickels and there are twice as many pennies as there are dimes. How many of each type of coin are there?​

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

the one with the highest speed