Answer:
8 small candles
16 large candles
Explanation:
1. Approach
Set up a system of equations to solve this problem. Call the number of small candles sold (x), and the number of large candles sold (y). Have one expression model the amount of money earned, the other model the number of candles sold. Then, solve this system of equations using the process of elimination. In the process of elimination, one multiplies one of the equations by a term such that one of the coefficients of a variable in one of the equations is the additive inverse of the corresponding variable in the other equation. This means that when one adds the two equations, one of the variables will eliminate. Then one can solve for the other variable, and finally, substitute the value of the variable that one found back into one of the equations, and solve for the value of the other variable.
2. Set up a system of equations
Use the given information to set up a system of equations to describe the amount earned, and the amount sold
x + y = 28 -> amount sold
4x + 6y = 144 -> amount earned
3. Solve the system
As explained above, the process of elimination is a method of solving a system of equations. In the process of elimination, one multiplies one of the equations by a term such that one of the coefficients of a variable in one of the equations is the additive inverse of the corresponding variable in the other equation. This means that when one adds the two equations, one of the variables will eliminate.
x + y = 28 (*-4)
4x + 6y = 144
-4x - 4y = -112
4x + 6y = 144
___________
2y = 32
/2 /2
y = 16
4. Solve to find out how much of the other candle was sold
Now back solve, substitute the found value into one of the equations, and solve to find the other value
x + y = 28
y = 16
x + 16 = 28
-16 -16
x = 8