Darius is comparing phone plans. If he chooses Cellular Unlimited, he could buy a phone for $390 and pay 7.50 $ per month for service. If he chooses Worldwide Wireless, he would pay 19.75 $ per month for service but would get a phone for free. In addition, Worldwide Wireless is offering new customers a $100 signing bonus. Which equation can you use to find m, the number of months it would take for the total cost to be the same for either plan? Choices: (A)7.5m + 390 = 19.75m + 100 (B)7.5m + 390 = 19.75m - 100 After how many months would the total cost be the same for either plan? Simplify any fractions. ____ months

Question

Darius is comparing phone plans. If he chooses Cellular Unlimited, he could buy a phone for $390 and pay 7.50 $ per month for service. If he chooses Worldwide Wireless, he would pay 19.75 $ per month for service but would get a phone for free. In addition, Worldwide Wireless is offering new customers a $100 signing bonus. Which equation can you use to find m, the number of months it would take for the total cost to be the same for either plan?   Choices: (A)7.5m + 390 = 19.75m + 100 (B)7.5m + 390 = 19.75m - 100  After how many months would the total cost be the same for either plan? Simplify any fractions.   ____ months

Bytelearn · Accepted Answer

Set Up Equation: Let's set up the equation for the total cost of each plan. For Cellular Unlimited, the total cost after m months would be the initial cost of the phone plus the monthly service fee times the number of months: 390 + 7.5m. For Worldwide Wireless, the total cost after m months would be the monthly service fee times the number of months minus the signing bonus: 19.75m - 100. We want to find when these two costs are equal.Write Equal Cost Equation: Now we write the equation that represents the point at which the costs are equal: 390 + 7.5m = 19.75m - 100.Subtract 7.5m: To solve for m, we need to get all the m terms on one side and the constants on the other. Let's subtract 7.5m from both sides of the equation: 390 = 19.75m - 7.5m - 100.Combine Like Terms: Now we combine like terms on the right side of the equation: 390 = 12.25m - 100.Add 100: Next, we add 100 to both sides to isolate the term with m: 390 + 100 = 12.25m.Add Numbers: We then add the numbers on the left side: 490 = 12.25m.Divide by 12.25: Finally, we divide both sides by 12.25 to solve for m: m = 490 / 12.25.Perform Division: Performing the division gives us the number of months: m = 40.

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