Aaron, Sarah and Neil travel a distance of 54.25 miles on a road trip. Neil drives the car for the greatest distance. Of the remaining distance, Sarah drives 18.4 miles, while Aaron drives one-third of the remaining distance.

Which equation can be used to determine the distance Neil drives, x?

I have worked on this question for 40 minutes straight it's driving me nuts man...

Question

Aaron, Sarah and Neil travel a distance of 54.25 miles on a road trip. Neil drives the car for the greatest distance. Of the remaining distance, Sarah drives 18.4 miles, while Aaron drives one-third of the remaining distance.

Which equation can be used to determine the distance Neil drives, x?

I have worked on this question for 40 minutes straight it's driving me nuts man...

anonymous · Answer

Neil's distance: x
Sarah's distance: 18.4
Aaron: 1/3 [54.25 - (x + 18.4)]

anonymous · Answer

How did you find Aaron's distance? (Or equation)

anonymous · Answer

x + 18.4 +  1/3 [54.25 - (x + 18.4)] = 54.25
Make sense?
Simplify the above and see what you get.

anonymous · Answer

"one-third of the remaining distance"
1/3 of the remaining disance
1/3 x [total distance - distance driven by Neil and Sarah"
1/3 [54.25 - (x + 18.4)]

anonymous · Answer

Oh! That makes much more sense!

anonymous · Answer

Lemme just simplify the other one

anonymous · Answer

Your question says "which equation". Is this multiple choice? Do you have the selections?

anonymous · Answer

Multiple Choice:


23(54.25−x)=18.4


(23)(54.25+x)=18.4


(23)(54.25)=18.4+x


(32)(54.25−x)=18.4

anonymous · Answer

(The "23" is 2/3 sorry about that, also goes for 32, 3/2)

anonymous · Answer

I also have hints if that helps:
Part 1
Try to find the expression for the distance that Aaron and Sarah drove between them.

Total distance is 54.25 miles and Neil drove x miles. Then how much did Sarah and Aaron drive?

Part 1
Of the remaining distance, Sarah drives 18.4 miles and Aaron a third of the remaining distance.

What fraction of the distance did Sarah drive?

Part 2
Two-third of (54.25−x) miles is 18.4. Express this sentence as an algebraic equation and solve for x.

anonymous · Answer

i'm sorry. i made a mistake.
Aaron's distance should be 1/3 (54.25 - x)
So that makes the equation:
   x + 18.4 +  1/3(54.25 - x) = 54.25

anonymous · Answer

it wouldn't make sense to say aaron drives 1/3 of remaining distance after Neil and Sarah. He drives 1/3 of the remaining distance just excluding Neil

anonymous · Answer

Thats absolutely fine! Dont worry about it! :D I really appreciate this so much!

anonymous · Answer

Also, could I combine the two x's? Or is there another step?