Let's call X the unit cost to the calls within Canada, Y the unit cost to the calls to U.S., and Z the unit cost to the calls to Brazil.
Based on the table we can formulate the following equations:
90X + 120Y + 180Z = 252
70X + 100Y + 120Z = 184
50X + 110Y + 150Z = 206
Then, to use the elimination method we need to multiply one equation by a number an add it to a second equation, so:
[tex]\begin{gathered} 90X+120Y+180Z=252 \\ \frac{-2}{3}(90X+120Y+180Z)=252\cdot(\frac{-2}{3}) \\ -60X-80Y-120Z=-168 \end{gathered}[/tex]
Then, adding this equation to the second one, we get:
-60X - 80Y - 120Z = -168
70X + 100Y + 120Z = 184
10X + 20 Y = 16
Repeating the process with the first and third equation:
[tex]\begin{gathered} \frac{-5}{6}(90X+120Y+180Z)=252\cdot(\frac{-5}{6}) \\ -75X-100Y-150Z=-210 \end{gathered}[/tex]
So:
- 75X - 100Y - 150Z = -210
50X + 110Y + 150Z = 206
-25X + 10Y = -4
Now, we can multiply the last equation by -2, adding with the previous one and solve for X as:
(-25X + 10Y)*(-2) = -4(-2)
50X - 20Y = 8
Then:
50X - 20Y = 8
10X + 20 Y = 16
60X = 24
X = 24/60
X = 2/5
Therefore, we can replace X by 2/5 and solve for Y as:
50X - 20Y = 8
50*(2/5) - 20Y = 8
20 - 20Y = 8
-20Y = 8 - 20
-20Y = - 12
Y = (-12)/(-20)
Y = 3/5
Finally, replacing X by 2/5 and Y by 3/5, we get that Z is equal to:
90X + 120Y + 180Z = 252
90*(2/5) + 120*(3/5) + 180Z = 252
36 + 72 +180Z = 252
108 + 180Z = 252
180Z = 252 - 108
180Z = 144
Z = 144/180
Z = 4/5
The unit cost to canada is Canada $0.4, to U.S. is $0.6, and to Brazil is $0.8
Answers: X = 2/5 = 0.4
Y = 3/5 = 0.6
Z = 4/5 = 0.8
