\begin{tabular}{l}\hline 4\( ) \) Listen \\ George wants to sign up for a new mobile phone plan. The mobile phone company offers George two plans. Mobile Green has a \\ monthly installment of \( \$ 20 \) plus an additional charge of 10 cents per gigabyte of data. Mobile Blue has a monthly installinent of \\ \( \$ 40 \) with an additional charge of 5 cents per gigabyte of data. \\ At how many gigabytes of data do the two plans cost the same amount, and what is that cost? \end{tabular}

To find the point at which the total costs of the two plans are equal, we can set up equations for both plans based on the given information. For Mobile Green: - Monthly cost = $20 + 0.10x, where \( x \) is the number of gigabytes. For Mobile Blue: - Monthly cost = $40 + 0.05x. Now, we want to find the number of gigabytes (\( x \)) where the costs are the same: \[ 20 + 0.10x = 40 + 0.05x. \] Now, we can solve for \( x \): 1. Rearranging gives us: \[ 0.10x - 0.05x = 40 - 20, \] which simplifies to \[ 0.05x = 20. \] 2. Dividing both sides by \( 0.05 \) results in: \[ x = 20 / 0.05 = 400. \] So, the two plans cost the same when George uses 400 gigabytes of data. To find the cost at this usage: - Substitute \( x = 400 \) into either plan: \[ \text{Cost for Mobile Green: } 20 + 0.10 \cdot 400 = 20 + 40 = 60. \] \[ \text{Cost for Mobile Blue: } 40 + 0.05 \cdot 400 = 40 + 20 = 60. \] Thus, both plans cost $60 when George uses 400 gigabytes of data.