One cell phone plan charges $20 per month plus $0.15 per minute used. A second cell phone plan charges $35 per month plus $0.10 per minute used. Write and solve an equation to find the number of minutes you must talk to have the same cost for both calling plans.

The equations are as follows where x represents the number of minutes the cell phone is used.

For plan one: Total cost = $20 + $0.15x

For plan two: Total cost = $35 + $0.10x

For both the costs to be the same, we need to use the cell phone for

300 minutes.

What are equations?

Equations are relations showing the value of one quantity related to another quantity when it can change. The changing value is the variable.

How do we solve the given question?

We are informed that one cell phone plan charges $20 per month plus $0.15 per minute used. A second cell phone plan charges $35 per month plus $0.10 per minute used.

We are asked to write and solve an equation to find the number of minutes you must talk to have the same cost for both calling plans.

Let the number of minutes the cell phone is used be x minutes.

Now we solve for equations for both plans in the following way:-

Plan one:

Charges $20 per month plus $0.15 per minute used.

When the use is for x minutes, the additional charge = $0.15*x = $0.15x

∴ Total cost = Fixed cost + Additional cost

or, Total cost = $20 + $0.15x.

Plan two:

Charges $35 per month plus $0.10 per minute used.

When the use is for x minutes, the additional charge = $0.10*x = $0.10x

∴ Total cost = Fixed cost + Additional cost

or, Total cost = $35 + $0.10x.

We are asked to find the number of minutes used so that the costs in both the plans are equal. To find this we equate the equation of total costs in both the cases to get:

$20 + $0.15x = $35 + $0.10x.

Subtracting ($20 + $0.10x) from both sides of the equation, we get

$20 + $0.15x - ($20 + $0.10x) = $35 + $0.10x - ($20 + $0.10x).

or, $20 + $0.15x - $20 - $0.10x = $35 + $0.10x - $20 - $0.10x.

or, $0.05x = $15

Dividing both sides of the equation by $0.05, we get

$0.05x/$0.05 = $10/$0.05

or, x = 300.

∴ We must talk for 300 minutes for both the plans to cost the same to us.

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