Justify your Answer. Geometry

Question

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. (Please make a short answer)

Answer 1

Well, the answer cannot be short because you left out the sign in the middle of

the first expression.

Suppose it is PLUG. Then

12x+106 + 5x+685 = 2500

17x + 791 = 2500

17x = 2500 - 791

17x = 2500-800+9

17x = 1709

x = 1709/17

plugging these in, the mileages are 1312+ and 1187+

so this is NOT the halfway point

BUT if you change the sign on the left side

of the equation from + to -, then the problem

becomes:

12x-106 + 5x + 685 = 2500

17x + 579 = 2500

17x = 2500-579

= 2500-500-79

= 2000-79

= 1900 + 100 - 79

= 1921

x= 1921/17 = 113

This is the halfway point, as each mileage becomes 1250

we plugged in

see watch

12(113)-106 = 12(100+13)-106 = 1200 + 156-106 = 1250

5(113)+685 = 565 + 685 = 1250

So from his home in South Carolina to Oldham county Texas is 12x - 106 = 1250 when x=113

and that is the halfway point.