Judy is selling small candles at the fair for $4 each and large candles for $6 each. She collected $144 selling a total of 28 candles. How many of each candle did she sell? Use x for the small candles and y for the large candles.

Let x = the number of small candles sold
Let y = the number of large candles sold

You are given two pieces of information:

(1) Number of candles sold: x + y = 28
(2) Revenue based on cost per candles sold: 4x + 6y = 144

Two equations, two unknowns - Solving by substitution (x = 28 - y)

4 * (28-y) + 6y = 144
112 - 4y + 6y = 144
112 + 2y = 144
2y = 32
y = 16

If y = 16, back substitute to find x = 12

Double check using revenue generated:

4x + 6y = 144
4(12) + 6(16) =? 144
48 + 96 = 144

Resolved: 12 small candles, 16 large candles.