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

Answer 1

We need to find an equation for each situation. Let x be the number of GB of data used.

Statement 1: At Noise Pollution Cellular, plan A is $30.00 per month and $5.00 for every gigabyte of data used.

Plan A cost equation $C(x) = 30 + 5x$

Statement 2: At Noise Pollution Cellular, Plan B is $50.00 per month and $2.00 for every gigabyte of data used.

Plan B cost equation $C(x) = 50 + 2x$

Number of GB of data for which both the plan A and plan B cost are same.

$30+5x=50+2x \\ Subtracting \; 2x \; \& \;30\; on\; both\; sides\; \\ \\30+5x-2x-30=50-30+2x-2x \\Combining \; like \; terms\\\\3x=20\\Dividing \; like \; terms\\\\ \frac{3x}{3}=\frac{20}{3} \\ \\x=6\frac{2}{3}$

When

$x=6 \\\\ Plan \; A \; Cost = 30+5(6)=30+30=\ 60\\ Plan \; B \; Cost = 50+2(6)=50+12= \ 72\\ \\ From \; 5\leq x\leq 6\frac{2}{3} , \; Plan \; A \; is \; Cheaper!$

When

$x = 7\\\\ Plan \; A \; Cost= 30 + 5(7) =30+35 = \ 65\\\\Plan \; B \; Cost = 50 + 2(7)=50+14=\ 64 \\ \\ From \; 6\frac{2}{3} \leq x \leq 8, \; Plan\; B \; is \; Cheaper !$

Answer 2

The best plan would be Plan B.