Answer:
(7, 5)
(0, 0)
(21, 15)
Step-by-step explanation:
We are given that Seth hiked 3.5 miles each hour, while David hiked 2.5 miles each hour.
As the x-coordinate represents the total distance, in miles, Seth hiked, and the y-coordinate represents the total distance, in miles, David hiked, then the ratio of the distances Seth and David hiked per hour can be expressed as:
[tex]x : y = 3.5 : 2.5[/tex]
This can be simplified to:
[tex]\dfrac{x}{y}=\dfrac{3.5}{2.5}\\\\\\ \dfrac{x}{y}=\dfrac{7}{5} \\\\\\ 5x=7y \\\\\\y=\dfrac{5}{7}x[/tex]
Now, we can check each of the given ordered pairs to see if they satisfy this equation:
[tex]x=7:\quad y=\dfrac{5}{7}\cdot 7=5 \quad \implies (7,5) \;\;\checkmark[/tex]
[tex]x=14:\quad y=\dfrac{5}{7}\cdot 14=10 \quad \implies (14,10) \;\; \mathcal{X}[/tex]
[tex]x=10:\quad y=\dfrac{5}{7}\cdot 10=7.14 \quad \implies (10,7.14) \;\; \mathcal{X}[/tex]
[tex]x=0:\quad y=\dfrac{5}{7}\cdot 0=0 \quad \implies (0,0) \;\;\checkmark[/tex]
[tex]x=21:\quad y=\dfrac{5}{7}\cdot 21=15 \quad \implies (21,15) \;\;\checkmark[/tex]
So, the ordered pairs that represent the relationship between the number of miles Seth and David hiked are:
