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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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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 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 [email protected] » 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.