eth hiked 3.5 miles each hour, while
David hiked 2.5 miles each hour.
Ordered pairs were graphed of the
total distance each boy hiked. The
x-coordinate represents the total
distance, in miles, Seth hiked, and
the y-coordinate represents the total
distance, in miles, David hiked. Select
all of the ordered pairs that represent
this relationship.
(7, 5) (14, 20)
(10, 14) (0, 0)
(21, 15)



Answer :

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:

  • (7, 5)
  • (0, 0)
  • (21, 15)
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