Select one of the options below and create a linear equation to represent the mo
ID: 3034705 • Letter: S
Question
Select one of the options below and create a linear equation to represent the monthly bill. When will the plans cost the same? Explain when each plan is a better option.
Option 1: Plan A $39.99 for 200 min and $1.25 for each min after. Plan B $29.99 for 200 min and $1.50 for each min after.
Option 2: Plan A $25.75 plus $.75 per min. Plan B $20.99 plus $1.00 per min
Option 3: Plan A $39.99 plus $1.25 per min. Plan B $25.99 plus $1.75 per min
Option 4: Plan A $45.99 for 400 min and $.50 for each min after. Plan B $49.99 for 400 min and $.40 for each min after
Explanation / Answer
Option 1:
Plan A: y = 1.25x + 39.99 where x is the number of minutes after first 200 minutes and y is the total cost for the entire talk time.
Plan B: y = 1.50x + 29.99
The plans A and B will cost the same if 1.25x + 39.99 = 1.50x + 29.99 or, 1.50x -1.25x = 39.99-29.99 or, 0.25x = 10 or x = 40. Thus, the two plans will cost the same if one talks for 240 minutes. For the first 200 minutes, plan B is better. and beyond 240 minutes, plan A is better.1
Option 2:
PlanA: y = 0.75x + 25.75
Plan B: y = x+20.99
The plans A and B will cost the same if 0.75x + 25.75 = x +20.99 or, 0.25x = 4.76 or x = 19.04. Thus, the two plans will cost the same if one talks for 19.04 minutes beyond the minimum talk time ( not mentioned here). For upto the minimum talk time + 19.04 minutes, plan B is better and beyond the minimum talk time + 19.04 minutes, plan A is better.
Option 3:
Plan A: y = 1.25x + 39.99
PlanB: y = 1.75x + 25.99
The plans A and B will cost the same if 1.25x + 39.99 = 1.75x + 25.99 or, 0.5x = 10 or x = 20. Thus, the two plans will cost the same if one talks for 20 minutes beyond the minimum talk time ( not mentioned here). For upto the minimum talk time + 20 minutes, plan B is better and beyond the minimum talk time + 20 minutes, plan A is better.
Option 4:
Plan A: y = 0.5x+ 45.99
Plan B: y = 0.4x+ 49.99
The plans A and B will cost the same if 0.5x + 45.99 = 0.4x + 49.99 or, 0.1x = 4 or x = 40. Thus, the two plans will cost the same if one talks for 440 minutes .For upto 400 minutes, plan A is better and beyond 440 minutes, plan B is better.
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