One cell phone plan allows 200 text messages per month for $20 after which text messages cost $0.04 each. Another cell plan allows 400 text essages per month for $30 each. What would be the minimum text messages that would justify the more expensive plan

I assume plan B is a flat $30/month. If so, the costs are equal for x minutes if

20+0.04(x-200) = 30

And the question is poorly worded.

To find the minimum text messages that would justify the more expensive plan, we need to compare the cost of sending the same number of text messages on both plans.

Let's assume we want to compare the plans by sending x number of text messages per month.

For the first plan, we have 200 text messages included in the $20 base price. Any additional text message beyond that costs $0.04 each. Therefore, for x text messages:
Cost on first plan = $20 + ($0.04 * (x - 200))

For the second plan, we have 400 text messages included in the $30 base price. Any additional text message beyond that has no extra charge. Therefore, for x text messages:
Cost on second plan = $30

Now, to determine when the second plan becomes justified, we need to find the point where the cost on the first plan surpasses the cost on the second plan.

So, we set the equation:
$20 + ($0.04 * (x - 200)) = $30

Simplifying this equation, we get:
$0.04 * (x - 200) = $30 - $20
$0.04 * (x - 200) = $10

Next, we divide both sides by $0.04 to isolate x:
x - 200 = $10 / $0.04
x - 200 = 250
x = 250 + 200
x = 450

Hence, the minimum number of text messages that would justify the more expensive plan is 450.