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?

Guest Oct 6, 2021

#1**0 **

*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**.

__Check answer:__

3/5 of 90 is 54. That leaves 36 miles. 2/3 of 36 is 24. That leaves 12 miles. Answer checks out.

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Guest Oct 6, 2021