I have 8 pennies and some quarters, nickels, and dimes. The number of pennies plus nickels equals the number of dimes. I have 3 quarters for every 2 pennies and 3 dimes for every 2 quarters. How many coins are nickels?

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

Answer:8 pennies, 12 quarters, 18 dimes, so there are 10 nickels