Final answer:
To determine when the two Verizon data plans cost the same, we solve the equation 200 + 5g = 300 + 2g for 'g'. We find that at exactly 33.33 gigabytes the costs are equal. However, rounding up, we conclude that at 40 gigabytes, option (A), the second plan becomes cheaper.
Step-by-step explanation:
To find out how many gigabytes of data you need to use for the prices of Verizon's two data plans to be equal, we set up an equation that represents the total cost of each plan. Let ‘g’ be the number of gigabytes of data used. The cost of the first plan is the $200 phone upgrade plus $5 per gigabyte, which can be written as 200 + 5g. The cost of the second plan is the $300 phone upgrade plus $2 per gigabyte, which can be written as 300 + 2g.
We want to find the point where the costs are the same, so we set up the equation:
200 + 5g = 300 + 2g
Now, we solve for 'g' by subtracting 2g from both sides:
200 + 3g = 300
Next, we subtract 200 from both sides:
3g = 100
We then divide both sides by 3 to find 'g':
g = 33.33
Since we need a whole number of gigabytes, we round up to the nearest whole gigabyte, which gives us:
g = 34 gigabytes
However, none of the options (A: 40 gigabytes, B: 50 gigabytes, C: 75 gigabytes, D: 100 gigabytes) is exactly 34 gigabytes. But since the student has to select the closest option, 40 gigabytes is the answer that makes the two plans equal in terms of cost, or the least number of gigabytes where the second plan ($300 upgrade + $2/gigabyte) becomes more favorable. With 40 gigabytes, the costs would be:
First plan: 200 + (5*40) = $400
Second plan: 300 + (2*40) = $380
Thus, the second plan with 40 gigabytes of data used is cheaper, and beyond that point, it remains cheaper than the first plan.