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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?7.5m+390=19.75m–1007.5m+390=19.75m+100After how many months would the total cost be the same for either plan?Simplify any fractions. monthsSubmit

Question

Darius is comparing phone plans. If he chooses Cellular Unlimited, he could buy a phone for 390andpay390 and pay 7.50 per month for service. If he chooses Worldwide Wireless, he would pay 19.75permonthforservicebutwouldgetaphoneforfree.Inaddition,WorldwideWirelessisofferingnewcustomersa19.75 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?7.5m+390=19.75m–1007.5m+390=19.75m+100After how many months would the total cost be the same for either plan?Simplify any fractions. monthsSubmit

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Solution

The equation to find m, the number of months it would take for the total cost to be the same for either plan, would be:

7.5m + 390 = 19.75m + 100

This is because with Cellular Unlimited, Darius would pay 390upfrontforthephoneandthen390 upfront for the phone and then 7.50 per month. With Worldwide Wireless, he would get a 100signingbonusandthenpay100 signing bonus and then pay 19.75 per month, but he wouldn't have to pay for the phone.

To find out after how many months the total cost would be the same for either plan, you would solve the equation for m:

First, subtract 7.5m from both sides to get:

390 - 100 = 19.75m - 7.5m

Then simplify to get:

290 = 12.25m

Finally, divide both sides by 12.25 to solve for m:

m = 290 / 12.25

Simplify the fraction to get:

m ≈ 23.67

So, it would take approximately 24 months (rounding up because you can't have a fraction of a month) for the total cost to be the same for either plan.

This problem has been solved

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