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4. Samuel is planning a walking tour of his city and is researching three different tour-guide
companies. The cost y of each company is a linear function of the number of hours x
that someone spends on the tour. The prices for three different companies are shown. Samuel
plans his tour for 6 hours and wants to spend the lesser amount of money. From which
company should he choose to do his walking tour?
Hidden Treasures
Walking Tour
y=9x + 25
Tipyy Tours
to ton
Road-Less-Traveled Tours
Cost ($), y
12
24
Hours, x
1
2
Part 2 y = 9(6) + 25 =54+28
(798)
70
50
30
Гу
10
Bowman Bros.
(3, 50)
(1, 30)
12= 12(1)
9(6) +25 6=0 24-12"
X
1 2 3 4 5 6 7
Hours

Answer 1

Samuel should choose Hidden Treasures Walking Tour for his 6-hour walking tour, since it offers the lowest cost at 79 dollars compared to the other companies.

Step-by-step explanation:

The student is asking about choosing the most cost-effective walking tour company based on linear equations representing the cost for different companies' services. Samuel plans a 6-hour tour and wants to find the company that will charge the least amount of money. The price for Hidden Treasures Walking Tour is given by the linear equation y = 9x + 25. The company Road-Less-Traveled Tours shows a graph from which we need to determine the cost equation, and the Bowman Bros.' costs can be determined from two data points given in the question: (1, 30) and (3, 50). To determine the most cost-effective option, we must calculate the total cost for a 6-hour tour for each company.

For Hidden Treasures Walking Tour, the cost for 6 hours is:

y = 9(6) + 25 = 54 + 25 = 79 dollars

To find the cost equation for Road-Less-Traveled Tours, we use the given points on the graph. The cost per hour is the rise over run between the two points (24 - 12) / (2 - 1) = 12 dollars per hour, and the y-intercept is 12 dollars since it crosses the y-axis at (0,12). Therefore, the equation is y = 12x + 12. The cost for a 6-hour tour would be:

y = 12(6) + 12 = 72 + 12 = 84 dollars

For Bowman Bros., we can use the two points to determine the slope (cost per hour) which is (50 - 30) / (3 - 1) = 20 / 2 = 10 dollars per hour. The y-intercept (starting fee) can be found by extending the line through the two points to where it crosses the y-intercept. Alternatively, we can use the point-slope form to calculate it:

50 = 10(3) + b => b = 50 - 30 = 20

So the Bowman Bros.' equation is y = 10x + 20. The cost for a 6-hour tour would be:

y = 10(6) + 20 = 60 + 20 = 80 dollars

Comparing all three costs, Samuel should choose Hidden Treasures Walking Tour which will cost him 79 dollars, as it is the cheapest option for a 6-hour tour.