Answer: Yes, Josh's parent's house in Texas is the midpoint between South Carolina and California.
Solution:
Distance from South Carolina to California: d=2,500 miles
Distance from South Carolina to Josh's parent's house in Texas: d1=12x-106
Distance from Josh's parent's house in Texas to California: d2=5x+685
Josh's parent's house in Texas is the midpoint between South Carolina and California if:
d1=d2=d/2→d1=d2=2,500 miles / 2→d1=d2=1,250 miles
Now, we know:
d1+d2=d
Replacing d1 by 12x-106; d2 by 5x+685; and d by 2,500:
(12x-106)+(5x+685)=2,500
12x-106+5x+685=2,500
Adding similar terms:
17x+579=2,500
Solving for x: Sutracting 579 both sides of the equation:
17x+579-579=2,500-579
17x=1,921
Dividing both sides of the equation by 17:
17x/17=1,921/17
x=113
With x we can calculate d1 and d2
d1=12x-106→d1=12(113)-106→d1=1,356-106→d1=1,250
d2=5x+685→d2=5(113)+685→d2=565+685→d2=1,250
Like d1=d2=1,250, Josh's parent's house in Texas is the midpoint between South Carolina and California
