Brad is taking his family on a vacation to the mountains, and he is deciding on a cabin to rent. The cabins at Rainbow Peak cost $104 per night, plus a one-time fee of $43 for service and cleaning. The cabins at Verdant Meadows cost $66 per night, plus a one-time fee of $195. Which equation can you use to find n, the number of nights the vacation would need to last for the two cabins to cost the same? Choices: (A)104n + 43 = 66n + 195 (B)104n + 66 = 195n + 43 How many nights would the vacation need to last for the two cabins to cost the same? ____ nights

Question

Brad is taking his family on a vacation to the mountains, and he is deciding on a cabin to rent. The cabins at Rainbow Peak cost $104 per night, plus a one-time fee of $43 for service and cleaning. The cabins at Verdant Meadows cost $66 per night, plus a one-time fee of $195. Which equation can you use to find n, the number of nights the vacation would need to last for the two cabins to cost the same?   Choices: (A)104n + 43 = 66n + 195 (B)104n + 66 = 195n + 43  How many nights would the vacation need to last for the two cabins to cost the same?   ____ nights

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Calculate Total Cost: To find the equation that represents the cost of staying at Rainbow Peak, we multiply the cost per night by the number of nights n and add the one-time fee. This gives us the total cost for Rainbow Peak as a function of n. Calculation: Total cost for Rainbow Peak = 104n + 43Find Cost Equations: Similarly, to find the equation that represents the cost of staying at Verdant Meadows, we multiply the cost per night by the number of nights n and add the one-time fee. This gives us the total cost for Verdant Meadows as a function of n. Calculation: Total cost for Verdant Meadows = 66n + 195Set Equations Equal: To find the number of nights n where the cost of both cabins is the same, we set the total cost equations equal to each other. Calculation: 104n + 43 = 66n + 195Solve for n: Now we need to solve for n. To do this, we will subtract 66n from both sides to get all the n terms on one side. Calculation: 104n - 66n + 43 = 195Combine Like Terms: Simplifying the equation by combining like terms gives us the equation with n on one side. Calculation: 38n + 43 = 195Isolate n Term: Next, we subtract 43 from both sides to isolate the term with n. Calculation: 38n = 195 - 43Perform Subtraction: Performing the subtraction gives us the value we need to find n. Calculation: 38n = 152Divide Both Sides: Finally, we divide both sides by 38 to solve for n. Calculation: n = 152 / 38Final Number of Nights: Performing the division gives us the number of nights. Calculation: n = 4

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