A family is visiting 5 states within 10 days for vacation. There are 4 people in the family. They have the option to travel 304 miles on the first day and visit 1 national park and 2 lakes. Or they can travel 260 miles to see a water park and an amusement park that each cost all ages $5. The national park costs $25 per vehicle and the 2 lakes are free. The next 3 days, they travel 284 miles and relaxed by the pool. The family vehicle can go 300 miles on a tank of gas worth $40. The last 4 days, they spend driving the same route back home and stopping at popular sightseeing landmarks.On the first day, how much does the cheaper route cost? Round your answer to the nearest cent and do not include $ in the answer. For example, if the cost is $19.01, put 19.01.

Accepted Solution

Answer:9.14Step-by-step explanation:The family vehicle can go 300 miles on a tank of gas worth $40. 1. Find the cost of the gas in two options for Day 1.First option:300 miles - $40304 miles - $xWrite a proportion:[tex]\dfrac{300}{304}=\dfrac{40}{x}\\ \\300x=304\cdot 40\\ \\30x=304\cdot 4\\ \\30x=1,216\\ \\x=\dfrac{1,216}{30}=\dfrac{608}{15}\approx 40.53[/tex]Second option:300 miles - $40260 miles - $yWrite a proportion:[tex]\dfrac{300}{260}=\dfrac{40}{y}\\ \\300y=260\cdot 40\\ \\3y=26\cdot 4\\ \\3y=104\\ \\=xy\dfrac{104}{3}\approx 34.67[/tex]2. Calculate the total price:First option:Gas cost = $40.53National park = $25Lakes - freeTotal cost = $65.53Second option:Gas cost = $34.67Water park for 4 persons [tex]=4\cdot \$5=\$20[/tex]Amusement park for 4 persons [tex]=4\cdot \$5=\$20[/tex]Total cost =$74.67Difference = $74.67 - $65.53 = $9.14