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Cell phone provider A charges $60 a month for 1 gigabyte (GB) of data plus $0.05 for each megabyte (MB) of overage data. Cell phone provider B charges $45 a month for 1GB of data plus $0.10 for each MB of overage data. Assuming there will be data overage, how many MB of overage data would make the cost of both data plans the same?

Cell phone provider A charges $60 \$ 60 a month for 11 gigabyte (GB) of data plus $0.05 \$ 0.05 for each megabyte (MB) of overage data. Cell phone provider B charges $45 \$ 45 a month for 1 GB 1 \mathrm{~GB} of data plus $0.10 \$ 0.10 for each MB of overage data. Assuming there will be data overage, how many MB of overage data would make the cost of both data plans the same?

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Q. Cell phone provider A charges $60 \$ 60 a month for 11 gigabyte (GB) of data plus $0.05 \$ 0.05 for each megabyte (MB) of overage data. Cell phone provider B charges $45 \$ 45 a month for 1 GB 1 \mathrm{~GB} of data plus $0.10 \$ 0.10 for each MB of overage data. Assuming there will be data overage, how many MB of overage data would make the cost of both data plans the same?
  1. Set up the equation: Set up the equation to represent the total cost for each provider.\newlineProvider A's cost for overage data is $0.05\$0.05 per MB, and Provider B's cost for overage data is $0.10\$0.10 per MB. Let's denote the number of MB of overage data as mm. The total cost for each provider will be the base cost plus the overage cost.\newlineFor Provider A: Total cost = $60+$0.05m\$60 + \$0.05m\newlineFor Provider B: Total cost = $45+$0.10m\$45 + \$0.10m
  2. Equate the total costs: Equate the total costs to find the point where they are the same.\newline60+0.05m=45+0.10m60 + 0.05m = 45 + 0.10m
  3. Subtract to isolate terms: Subtract $45\$45 from both sides to isolate the terms with ＂m＂. \newline$60−$45+$0.05m=$45−$45+$0.10m\$60 - \$45 + \$0.05m = \$45 - \$45 + \$0.10m \newline$15+$0.05m=$0.10m\$15 + \$0.05m = \$0.10m
  4. Solve for m: Subtract $0.05m\$0.05m from both sides to solve for mm.\newline$15=$0.10m−$0.05m\$15 = \$0.10m - \$0.05m \newline$15=$0.05m\$15 = \$0.05m
  5. Divide to find overage data: Divide both sides by $0.05\$0.05 to find the number of MB of overage data.\newline$15$0.05=$0.05m$0.05\frac{\$15}{\$0.05} = \frac{\$0.05m}{\$0.05} \newline300=m300 = m \newline 300300 MB of overage data would make the cost of both data plans the same.

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