Max Points: 5.0 Select one of the options below and create a tinear equation to
ID: 2339072 • Letter: M
Question
Max Points: 5.0 Select one of the options below and create a tinear equation to represent the monthly bill When will the plans cost the same? Admin Explain when each plan is a better option. Option 1: Plan A 539.99 for 200 min and $1.25 for each min after. Plan B $29.99 for 200 min and 51.50 for each min after Option 2: Plan A $25.75 plus $.75 per min. Plan 8 $20.99 plus S1.00 per min Option 3: Plan A S39.99 plus $1.25 per min. Plan B $25.99 plus 1.75 per min option 4: Plan A $45,99 for 400 min and S.50 for each min after. Plan B $49.99 for 400 min and S.40 for each min afterExplanation / Answer
Let us select the option 3.
Let the variable x represents the minutes
The format of linear equation is a+bx, where x is dependent variable, minute.
Plan A:
Total Monthly bill = $39.99 + $1.25x
Plan B:
Total monthly bill = $25.99 + $1.75x
For plans to cost the same, their monthly bills should be equal:
Hence, Total monthly bill plan A = Total monthly bill plan B
$39.99 + $1.25x = $25.99 + $1.,75x
it gives, $1.75x -$1.25x = $39.99 - $25.99
it gives, $0.5x = $14
it gives, x= $14 / $0.5
it gives, x= 28
so, in 28 minutes of time, both plans will give the same cost.
For better option, we will put values (greater than 28) in x or minutes in the linear equation of plan A and plan B. Let us calculate the linear equation of plan A and plan B with values of x = 25,27,30,35
Let us assume x= 25 minutes, then,
Plan A monthly bill = $39.99 + $1.25 (25)
= $71.24
Plan B monthly bill = $25.99 +$1.75 (25)
= $69.74
Now,
Let us assume x= 27 minutes, then,
Plan A monthly bill = $39.99 + $1.25 (27)
= $71.74
Plan B monthly bill = $25.99 +$1.75 (27)
= $73.24
Let us assume x= 30 minutes, then,
Plan A monthly bill = $39.99 + $1.25 (30)
= $77.49
Plan B monthly bill = $25.99 +$1.75 (30)
= $78.49
Let us assume x= 35 minutes, then,
Plan A monthly bill = $39.99 + $1.25 (35)
= $83.74
Plan B monthly bill = $25.99 +$1.75 (35)
= $87.24
So we can conclude that when x or minutes are more than 28, than plan A has lesser monthly bill than plan B, so, plan A is better.
And, if x or minutes are less than 28, than plan B has lesser monthly bill than plan A so plan B is better.