Josh wilson is traveling to california from south carolina for summer vacation. the states are approximately 2500 miles apart driving cross-country. he stops at his parent's house in oldham county, texas, which is (12x 106) miles away from south carolina and (5x + 685) miles away from california. determine if josh's parent's house in texas the midpoint between south carolina and california? justify your 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

the answer is c)8

step-by-step explanaction: