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Rama09 [41]
3 years ago
13

Josh Wilson is traveling to California from South Carolina for summer vacation. The states are approximately 2500 miles apart dr

iving 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.
Mathematics
2 answers:
grandymaker [24]3 years ago
8 0

Answer:

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

Step-by-step explanation:

Let S represents South carolina C represents California and T represents Texas,

Given,

ST = 12x - 106,

TC = 5x + 685,

Also, SC = 2500 miles,

Suppose T is the midpoint of S and C,

⇒ ST = TC

12x - 106 = 5x + 685

7x = 791

⇒ x = \frac{791}{7} = 113

So, ST = 12(113)+106 =1356 - 106 = 1250

Now,

2\times ST = 2\times 1250=2500

⇒ 2 ST = SC

Hence, T is the midpoint of S and C.

MakcuM [25]3 years ago
5 0

Given, distance between South Carolina and Texas = 12x-106

Distance between Texas and California = 5x+685

Let's assume, both the distance is same.

12x-106=5x+685

=> 12x-5x = 685+106

=> 7x = 791

=>x=113

Plug x = 113 in 5x+685

5(113)+685 = 1250 Miles.

Similarly, 12(113)-106=1250 miles

Since 2500 divided by 2 = 1250 miles, hence our assumption was correct, Texas lies between both the cities.

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