There are some nickels, dimes, and quarters in a large piggy bank. For every 2 nickels there dimes. For every 2 dimes there are 5 quarters. There are 500 coins total. a. How many nickels, dimes, and quarters are in the piggy bank? Explain your reasoning.

Let the equation be: n + d + q = 500 let this be 1 n/2 = d/3 (for every 2 nickels there are 3 dimes) let this be 2 d/2 = q/5 (for every 2 dimes, there are 5 quarters) let this be 3   from 2, n = 2/3d   from 3, q = 5/2d   substitute the given values into equation 1:   2/3d + d + 5/2d = 500   Multiply by 6 both sides   4d + 6d + 15d = 3000   25d = 3000   d = 3000/25   d = 120   answer: 120 dimes, 2/3 x 120 = 80 nickels and 5/2 x 120 = 300 quarters.