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A plane was originally flying at an altitude of x feet when it ascended 2,000 feet and then descended 5,000 feet. If

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by BTGmoderatorDC » Wed Jul 13, 2022 6:45 pm

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A plane was originally flying at an altitude of x feet when it ascended 2,000 feet and then descended 5,000 feet. If the plane's altitude after these two changes was 1/3 its original altitude, then the solution of which of the following equations gives the plane's original altitude, in feet ?

(A) x + 2000 = 1/3*(x - 3000)
(B) 1/3*(x - 3000) = x
(C) x + 3000 = 1/3*x
(D) x - 7000 = 1/3*x
(E) x - 3000 = 1/3*x


OA E

Source: Princeton Review
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Re: A plane was originally flying at an altitude of x feet when it ascended 2,000 feet and then descended 5,000 feet. If

by swerve » Sun Jul 24, 2022 2:44 pm
BTGmoderatorDC wrote: ↑
Wed Jul 13, 2022 6:45 pm
 A plane was originally flying at an altitude of x feet when it ascended 2,000 feet and then descended 5,000 feet. If the plane's altitude after these two changes was 1/3 its original altitude, then the solution of which of the following equations gives the plane's original altitude, in feet ?

(A) x + 2000 = 1/3*(x - 3000)
(B) 1/3*(x - 3000) = x
(C) x + 3000 = 1/3*x
(D) x - 7000 = 1/3*x
(E) x - 3000 = 1/3*x


OA E

Source: Princeton Review
The plane starts at altitude \(x\).
The altitude then increases \(2000 \,\text{ft}\, (x+2000)\).
It then decreases \(5000\, \text{ft}\) from there \(((x+2000)-5000))\). Net change\(= x-3000\)
This is equal to \(\dfrac{1}{3}\) of \(x\). Set both equations equal:
\(x-3000=\dfrac{1}{3}x\)
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Re: A plane was originally flying at an altitude of x feet when it ascended 2,000 feet and then descended 5,000 feet. If

by Scott@TargetTestPrep » Wed Dec 28, 2022 5:43 pm
BTGmoderatorDC wrote: ↑
Wed Jul 13, 2022 6:45 pm
 A plane was originally flying at an altitude of x feet when it ascended 2,000 feet and then descended 5,000 feet. If the plane's altitude after these two changes was 1/3 its original altitude, then the solution of which of the following equations gives the plane's original altitude, in feet ?

(A) x + 2000 = 1/3*(x - 3000)
(B) 1/3*(x - 3000) = x
(C) x + 3000 = 1/3*x
(D) x - 7000 = 1/3*x
(E) x - 3000 = 1/3*x


OA E

Source: Princeton Review
Solution:

The plane’s original altitude was x. After ascending 2,000 feet and descending 5,000 feet; the altitude of the plane became x + 2000 - 5000 = x - 3000. We are given that this was equal to 1/3 of its original altitude, so x - 3000 must equal 1/3*x. Thus, the equation that gives the plane’s original altitude is x - 3000 = 1/3*x.

Answer: E

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