You sell small candles for $4 each and large candles for $6 each. You collect $144 selling a total of 28 candles. How many of each type of candle did you sell?

Question

Method that must be used is by substitution 

Answer 1

My friends, this one is all about turning English into Algebra (labeling variables and solving accordingly)

 

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.

Answer 2

Let S= Number of small candles sold

L = Number of large candles 

 

S+L = 28 = total number of candles sold......... Eq 1

 

Amount collected for small candles= 4xS

Amount collected for Large candles = 6xL

Total amount collected = 4S +6L =144......... Eq 2

 

from Eq 1    L = 28 - S

 

Substituing this value in Eq 2

 

4S + 6 ( 28-S) = 144 

4S -6S = 144 -168

-2S = - 24 

2S =24 

Gives S = 12

Substituting the value of S in Eq 1

12 + L = 28

or L = 28 - 12 = 16

Number of Small sold =12

Number of large sold = 16