Answer: The cost of each small candle is $3 and the cost of each large candle is $6.
Explanation:
Let's use variables to represent the cost of each small candle and each large candle. Let's call the cost of each small candle "x" and the cost of each large candle "y".
We can set up two equations based on the information given:
4x + 1y = 18 (equation 1)
5x + 2y = 27 (equation 2)
We can solve for one variable in terms of the other by using one equation to eliminate one variable. Let's solve for "y" in terms of "x" by multiplying equation 1 by 2 and subtracting it from equation 2:
5x + 2y = 27
(8x + 2y = 36)
-3x = -9
Dividing both sides by -3, we get:
x = 3
Now that we know the cost of each small candle is $3, we can substitute that value into one of the equations to solve for the cost of each large candle. Let's use equation 1:
4x + 1y = 18
4(3) + 1y = 18
12 + y = 18
y = 6
Therefore, the cost of each small candle is $3 and the cost of each large candle is $6.