Question

Two cell phone plans offer differing text packages. The two plans are outlined below: Plan A: $9.25 per month charge along with a charge of $0.06 per text. Plan B: $2.50per month charge, but a charge of $0.20 per text. Is there a certain number of texts, when the two plans cost the same amount? Determine your answer by setting up a system of equations that model the two plans.

Answer 1

48

Explanation:

Let T be the number of texts sent on each plan.

The cost of Plan A can be represented as $9.25 + $0.06T.

The cost of Plan B can be represented as $2.50 + $0.20T.

We want to find the number of texts T at which the two plans cost the same amount. Therefore, we can set the two equations equal to each other and solve for T:

$9.25 + $0.06T = $2.50 + $0.20T

Subtracting $2.50 from both sides, we get:

$6.75 + $0.06T = $0.20T

Subtracting $0.06T from both sides, we get:

$6.75 = $0.14T

Dividing both sides by $0.14, we get:

T = 48.21

Therefore, the number of texts at which the two plans cost the same amount is approximately 48 texts. This means that if you send fewer than 48 texts per month, Plan A will be cheaper, and if you send more than 48 texts per month, Plan B will be cheaper.