There are five nickels.
Let w = the number of pennies; x = the number of nickels; y = the number of dimes; z = the number of quarters.
Then, we have three equations with four unknowns:
(1) w + x = y
(2) 3w = 2z
(3) 2y = 3z
However, there is a fourth unstated condition: w, x, y, and z must all be integers.
Assume that z = 6 (to avoid fractions).
From Equation (2), w = 4.
From Equation (3), y = 9.
Insert the values for w and y into equation (1).
4 + x = 9
x = 9 – 4 = 5
Thus, there are 4 pennies, 5 nickels, 9 dimes, and 6 quarters.
Check: 4 pennies + 5 nickels = 9 dimes
6 quarters + 4 pennies = 3 quarters for every 2 pennies
9 dimes + 6 quarters = 3 dimes for every 2 quarters
