Question

Ite Plane - Part 1

1. Josh is traveling from South Carolina to California for summer vacation. The states se
Carolina to Texas is represented by 12x
- 106. The distance from Texas to California is
approximately 2500 miles apart, so he makes a pitstop in Texas. The distance from south
represented by (5x + 685).
5x + 685
12x = 106
Is Josh's pitstop in Texas the midpoint between South Carolina and California? Justify your
answer.

Answer 1

Josh's parent's house in Texas is the midpoint between South Carolina and California.

Explanation

Let distance from South Carolina to California = D

D = 2,500 miles

Let distance from South Carolina to Josh's parent's house in Texas = D1

D1 = 12x - 106

Let distance from Josh's parent's house in Texas to California = D2

D2 = 5x + 685

Solve if Josh's parent's house in Texas is the midpoint between South Carolina and California

D1 = D2 = D/2

D/2 = 2,500 miles / 2

= 1,250 miles

D1 = D2 = 1,250 miles

D1 + D2 = D

Substituting D1 = 12x-106 and

D2 = 5x+685 and

D = 2,500

D1 + D2 = D

(12x-106) + (5x+685) = 2,500

Open parenthesis

12x - 106 + 5x + 685 = 2,500

Collecting like terms

12x + 5x = 2,500 - 685 + 106

17x = 1,921

Divide both sides by 17

x = 1,921 / 17

= 113

x = 113

Substitute x into D1 and D2

D1 = 12x - 106

D1 =12(113) - 106

= 1,356 - 106

D1 = 1,250

D2 = 5x + 685

D2 = 5(113) + 685

= 565 + 685

D2 = 1,250

Therefore, Josh's parent's house in Texas is the midpoint between South Carolina and California