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. This gives us the equation: Total cost for Cellular Unlimited = 390 + 7.5mCalculate Total Costs: For Worldwide Wireless, the total cost after m months would be the monthly service fee times the number of months minus the signing bonus, since the phone is free. This gives us the equation: Total cost for Worldwide Wireless = 19.75m - 100Set Equations Equal: To find the number of months m when the total cost for both plans is the same, we set the two total cost equations equal to each other: 390 + 7.5m = 19.75m - 100Solve for m: Now we need to solve for m. First, let's move all the terms involving m to one side of the equation and the constant terms to the other side. We can do this by subtracting 7.5m from both sides and adding 100 to both sides: 390 + 100 = 19.75m - 7.5mCombine Like Terms: Simplify the equation by combining like terms: 490 = 12.25mIsolate m: Now, divide both sides by 12.25 to isolate m: m = 490 / 12.25Perform Division: Perform the division to find the value of m: m = 40

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