Question

A cell phone company offers two texting plans. Plan A offers $2 monthly fee plus 10 cents for each text sent or received. Plan B offers $10 monthly fee plus 3 cents for each text sent or received. After how many texts would the cost of Plan A and B would be about the same?

Answer 1

After setting up equations representing the cost of both texting plans, Plan A ($2 + $0.10 per text) and Plan B ($10 + $0.03 per text), and solving for the number of texts where both plans cost the same, it is found that after approximately 114 texts, the cost of both plans would be about the same.

Step-by-step explanation:

To find out after how many texts the cost of Plan A and Plan B would be the same, we can set up an equation where the cost of both plans are equal. Let's denote the number of texts sent or received as 'x'.

For Plan A, the cost is given by the equation:
Cost of Plan A = $2 + $0.10x

For Plan B, the cost is given by the equation:
Cost of Plan B = $10 + $0.03x

To find the point at which both plans cost the same, we can set the cost equal to each other and solve for 'x':
$2 + $0.10x = $10 + $0.03x

After simplifying, we find:
$0.07x = $8
x = $8 / $0.07
x = 114.29

Therefore, after about 114 texts, the cost of the two cell phone company plans would be approximately the same.