Given:
Total distance = [tex]6\dfrac{1}{5}[/tex] miles
Hiking before lunch = [tex]2\dfrac{2}{3}[/tex] miles
To find:
How much further does Sylvia have left to hike?
Solution:
Let x be the remaining hiking distance.
We know that,
Total hiking distance = Hiking before lunch + Remaining hiking distance
[tex]6\dfrac{1}{5}=2\dfrac{2}{3}+x[/tex]
[tex]\dfrac{(6\times 5)+1}{5}=\dfrac{(2\times 3)+2}{3}+x[/tex]
[tex]\dfrac{30+1}{5}=\dfrac{6+2}{3}+x[/tex]
[tex]\dfrac{31}{5}=\dfrac{8}{3}+x[/tex]
Isolate variable term.
[tex]\dfrac{31}{5}-\dfrac{8}{3}=x[/tex]
[tex]\dfrac{93-40}{15}=x[/tex]
[tex]\dfrac{53}{15}=x[/tex]
It can be written as
[tex]\dfrac{45+8}{15}=x[/tex]
[tex]\dfrac{(3\times 15)+8}{15}=x[/tex]
[tex]3\dfrac{8}{15}=x[/tex]
So, [tex]3\dfrac{8}{15}[/tex] miles left to hike.
Therefore, the correct option is C.
