Question

two cell phone companies offer monthly plans.

• plan a: charges a base rate of r dollars plus $3 per gigabyte of data used.
• plan b: charges $2 per gigabyte plus a flat $8 fee.

if both plans cost the same for x gigabytes, the equation is: 3x + r = 2x + 8. solve for x in terms of r. if r = 6, determine the number of gigabytes where both plans cost the same

Explanation:

Step1: Rearrange the equation

Given $3x + r=2x + 8$. Subtract $2x$ from both sides: $3x-2x+r=2x - 2x+8$, which simplifies to $x+r = 8$.

Step2: Solve for x

Subtract $r$ from both sides of the equation $x+r = 8$. We get $x=8 - r$.

Step3: Substitute r = 6

When $r = 6$, substitute $r$ into $x=8 - r$. So $x=8 - 6=2$.

Answer:

$x = 8 - r$; both plans will cost the same at 2 gigabytes.