Question

At Noise Pollution Cellular, plan A is $30.00 per month and $5.00 for every gigabyte of data. Plan B is $50.00 per month and $2.00 for every gigabyte of data used. Irfan wants to find out which plan is the best choice for him. On average, he uses five to eight GB of data per month.



How much data would Irfan need to use for both plans to cost the same?

Answer 1

Answer:

Part 1) The best choice is Plan A

Part 2) The data is $6\frac{2}{3}\ GB$

Step-by-step explanation:

Part 1)

Let

y ----> the cost per month

x ----> the number of GB of data per month

we know that

Plan A

$y=5x+30$

Plan B

$y=2x+50$

Find out which plan is the best choice if he uses five to eight GB of data per month

Plan A

For x=5 GB -----> y=5(5)+30=$55

For x=8 GB -----> y=5(8)+30=$70

so

with Plan A the cost is between $55 and $70 -----> average $62.5

Plan B

For x=5 GB -----> y=2(5)+50=$60

For x=8 GB -----> y=2(8)+50=$66

so

with Plan B the cost is between $60 and $66 ----> average $63

therefore

The best choice is Plan A

Part 2) How much data would Irfan need to use for both plans to cost the same?

we have

y=5x+30 ----> equation A

y=2x+50 ----> equation B

Solve the system of equations by elimination

Subtract equation B from equation A

0=5x-2x+30-50

0=3x-20

3x=20

$x=\frac{20}{3}\ GB$

Convert to mixed number

$x=6\frac{2}{3}\ GB$ ----> for this data the cost is the same in both plans