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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?

104 n+66=195 n+43quad104 n+43=66 n+195
How many nights would the vacation need to last for the two cabins to cost the same?

◻ nights

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 \$ 104 per night, plus a one-time fee of $43 \$ 43 for service and cleaning. The cabins at Verdant Meadows cost $66 \$ 66 per night, plus a one-time fee of $195 \$ 195 .\newlineWhich equation can you use to find n n , the number of nights the vacation would need to last for the two cabins to cost the same?\newline104n+66=195n+43104n+43=66n+195 104 n+66=195 n+43 \quad 104 n+43=66 n+195 \newlineHow many nights would the vacation need to last for the two cabins to cost the same?\newline \square nights

Full solution

Q. 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 \$ 104 per night, plus a one-time fee of $43 \$ 43 for service and cleaning. The cabins at Verdant Meadows cost $66 \$ 66 per night, plus a one-time fee of $195 \$ 195 .\newlineWhich equation can you use to find n n , the number of nights the vacation would need to last for the two cabins to cost the same?\newline104n+66=195n+43104n+43=66n+195 104 n+66=195 n+43 \quad 104 n+43=66 n+195 \newlineHow many nights would the vacation need to last for the two cabins to cost the same?\newline \square nights
  1. Identify equation: Identify the correct equation to use for comparing the costs of the two cabins. The equation should equate the total costs of staying at Rainbow Peak and Verdant Meadows. The correct equation is 104n+43=66n+195104n + 43 = 66n + 195
  2. Simplify equation: Simplify the equation by subtracting 66n66n from both sides to isolate the terms with nn on one side. This gives 104n66n+43=195104n - 66n + 43 = 195. Simplifying further, 38n+43=19538n + 43 = 195
  3. Subtract to solve: Subtract 4343 from both sides to solve for nn. This results in 38n=15238n = 152

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