Question

A family is visiting 4 states within 10 days on vacation. They travel 304 miles on the first day and visit 1 national park and 2 lakes.The next 2 days, they travel 260 miles to see a water park and an amusement park. The next 3 days, they travel 284 miles and relaxed by the pool. The last 4 days, they spend driving the same route back home and stopping at popular sightseeing landmarks. What was the total number of miles they traveled?

Answer 1

9.14

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 - $40

304 miles - $x

Write a proportion:

\begin{lgathered}\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\end{lgathered}

304

300

=

x

40

300x=304⋅40

30x=304⋅4

30x=1,216

x=

30

1,216

=

15

608

≈40.53

Second option:

300 miles - $40

260 miles - $y

Write a proportion:

\begin{lgathered}\dfrac{300}{260}=\dfrac{40}{y}\\ \\300y=260\cdot 40\\ \\3y=26\cdot 4\\ \\3y=104\\ \\=xy\dfrac{104}{3}\approx 34.67\end{lgathered}

260

300

=

y

40

300y=260⋅40

3y=26⋅4

3y=104

=xy

3

104

≈34.67

2. Calculate the total price:

First option:

Gas cost = $40.53

National park = $25

Lakes - free

Total cost = $65.53

Second option:

Gas cost = $34.67

Water park for 4 persons =4\cdot \$5=\$20=4⋅$5=$20

Amusement park for 4 persons =4\cdot \$5=\$20=4⋅$5=$20

Total cost =$74.67

Difference = 74.67 -74.67−65.53 = $9.14

Answer 2

1696

Explanation:

304+260+284=848

848 * 2 =1696