Question

Paul is comparing the cost of cell phone services. At CellCoA, the phone he wants costs $305 and the unlimited calling plan costs $45 per month. At CellCoB, Paul can purchase the same phone for $350 and get an unlimited calling plan for $30 per month. In how many months will both plans cost the same?

These equations, which are graphed below, represent the situation.

y = 45x + 305

y = 30x + 350

Here, x represents the number of months and y represents the amount paid.



At
, both options will have cost him $
.

Answer 1

Paul will find that both cell phone services will cost the same amount after 3 months, totaling $440.

Step-by-step explanation:

To determine when both cell phone plans will cost the same amount, we need to find the point at which the two equations intersect. The equations given are:

• CellCoA: y = 45x + 305
• CellCoB: y = 30x + 350

By setting the two equations equal to each other, we can solve for x, which represents the number of months before the total costs are equal:

45x + 305 = 30x + 350

Now, we'll subtract 30x from both sides:

15x + 305 = 350

Next, we'll subtract 305 from both sides:

15x = 45

Finally, we'll divide both sides by 15:

x = 3

Therefore, after 3 months, both plans will have cost the same amount, which we can calculate:

y = 45(3) + 305

= 440

In this scenario, both options will have cost Paul $440 after 3 months.