Question

Alana is comparing the cost of cell phone services. The phone she wants costs $60 at Greenville Cellular, and the unlimited calling plan through their carrier would cost $1 per day. At Hartman Electronics, Alana could purchase the same phone for $40 and also get an unlimited calling plan for $3 per day. After some number of days, the two options would end up having the same total cost. How long would that take?

Answer 1

After setting up equations for the total cost of cell phone service from both Greenville Cellular and Hartman Electronics and solving for x, the number of days, we find that it will take 10 days for both options to cost the same.

Step-by-step explanation:

The question asks us to find out how many days it would take for the cost of cell phone services at Greenville Cellular and Hartman Electronics to be the same. To solve this, set up an equation representing the total cost for each option.

Let x represent the number of days after which the two options will cost the same.

Greenville Cellular option: Initial cost of phone ($60) + Daily cost ($1 × x) = $60 + $1x

Hartman Electronics option: Initial cost of phone ($40) + Daily cost ($3 × x) = $40 + $3x

To find the number of days where the costs are the same, set the two expressions equal to each other:

$60 + $1x = $40 + $3x

Subtract $1x from both sides:

$60 = $40 + $2x

Now subtract $40 from both sides:

$20 = $2x

Finally, divide both sides by $2 to solve for x:

$10 = x

So, after 10 days, the total cost for both the Greenville Cellular and Hartman Electronics options will be the same.