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# Math

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I traveled from Vertex Valley to Fraction Falls last week. I completed 3/5 of the distance in the morning and 2/3 of the remaining distance in the afternoon. I still had 12 miles to travel. What is the distance from Vertex Valley to Fraction Falls?

Oct 6, 2021

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I traveled from Vertex Valley to Fraction Falls last week. I completed 3/5 of the distance in the morning and 2/3 of the remaining distance in the afternoon. I still had 12 miles to travel. What is the distance from Vertex Valley to Fraction Falls?

Let X represent the total distance.

X  =  3/5 of the distance + 2/3 of the remaining 2/5 of the distance + 12

X  =  (3/5)X + (2/3)(2/5)X + 12

X  =  3X/5 + 4X/15 + 12        It's necessary to convert all the denominators to the same number.

X  =  (3/3)(3X/5) + 4X/15 + (15/15)(12)

X  =  9X/15 + 4X/15 + 180/15

X  =  (9X + 4X + 180) / 15      Next, to multiply both sides by 15

15X  =  9X + 4X + 180            Next, to combine 9X + 4X to 13X and subtract it from both sides.

2X  =  180

X  =  90                                The distance from Vertex Valley to Fraction Falls is 90 miles.