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When the price of oranges is lowered by 40%, 4 more oranges

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When the price of oranges is lowered by 40%, 4 more oranges [#permalink]

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New post Updated on: 08 Jul 2012, 06:22
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When the price of oranges is lowered by 40%, 4 more oranges can be purchased for $12 than can be purchased for the original price. How many oranges can be purchased for 24 dollars at the original price?

(A) 8
(B) 12
(C) 16
(D) 20
(E) 24

Originally posted by farukqmul on 08 Jul 2012, 06:19.
Last edited by Bunuel on 08 Jul 2012, 06:22, edited 1 time in total.
Edited the question.
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Re: When the price of oranges is lowered by 40%, 4 more oranges [#permalink]

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New post 08 Jul 2012, 06:33
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farukqmul wrote:
When the price of oranges is lowered by 40%, 4 more oranges can be purchased for $12 than can be purchased for the original price. How many oranges can be purchased for 24 dollars at the original price?

(A) 8
(B) 12
(C) 16
(D) 20
(E) 24


Say \(x\) is the original price of an orange, then:

\(xn=12\);
and
\(0.6x*(n+4)=12\) --> \(x(n+4)=20\) --> \(xn+4x=20\) --> \(12+4x=20\) --> \(x=2\).

So, for 24 dollars 24/2=12 oranges can be purchased at the original price of $2.

Answer: B.
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Re: When the price of oranges is lowered by 40%, 4 more oranges [#permalink]

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New post 15 Jul 2012, 03:22
Bunuel wrote:
farukqmul wrote:
When the price of oranges is lowered by 40%, 4 more oranges can be purchased for $12 than can be purchased for the original price. How many oranges can be purchased for 24 dollars at the original price?

(A) 8
(B) 12
(C) 16
(D) 20
(E) 24


Say \(x\) is the original price of an orange, then:

\(xn=12\);
and
\(0.6x*(n+4)=12\) --> \(x(n+4)=20\) --> \(xn+4x=20\) --> \(12+4x=20\) --> \(x=2\).

So, for 24 dollars 24/2=12 oranges can be purchased at the original price of $2.

Answer: B.

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Re: When the price of oranges is lowered by 40%, 4 more oranges [#permalink]

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New post 22 Oct 2016, 12:32
Set up:

12/p = x
12/0.60 = x+4

Manipulate and plug the first equation into the second --> you'll find p = $2

Thus $24/$2 per orange = 12 oranges
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Re: When the price of oranges is lowered by 40%, 4 more oranges [#permalink]

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New post 22 Oct 2016, 18:22
farukqmul wrote:
When the price of oranges is lowered by 40%, 4 more oranges can be purchased for $12 than can be purchased for the original price. How many oranges can be purchased for 24 dollars at the original price?

(A) 8
(B) 12
(C) 16
(D) 20
(E) 24


let r=number of oranges purchased originally
[12/(r+4)]/(12/r)=.6
r/(r+4)=.6
r=6 oranges
$12/6=$2 per orange
$24/$2=12 oranges
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Re: When the price of oranges is lowered by 40%, 4 more oranges [#permalink]

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New post 21 Apr 2017, 01:28
Here is what i did in this question =>

Let the price of each orange be $x
Hence for $12 => we can buy => 12/x oranges

Now new price => x(1-40/100) => $0.6x
Hence for $12 we could now buy => 12/0.6x


As per the given information => 12/x+4=12/0.6x
Hence 12+4x/x=20/x
=> 12+4x=20
=>x=2

So the price of each orange is $2

Now for 24 dollars => we can buy => 1/2*24=12 oranges

SMASH THAT B.

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Re: When the price of oranges is lowered by 40%, 4 more oranges [#permalink]

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New post 30 Jun 2018, 19:53
12/(.6x)=12/x+4
20=12+4x
x=2
24/2

Answer B
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Re: When the price of oranges is lowered by 40%, 4 more oranges [#permalink]

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New post 04 Jul 2018, 19:25
farukqmul wrote:
When the price of oranges is lowered by 40%, 4 more oranges can be purchased for $12 than can be purchased for the original price. How many oranges can be purchased for 24 dollars at the original price?

(A) 8
(B) 12
(C) 16
(D) 20
(E) 24


We use the equation: price per item x no. of items = total cost. Here, we let p = the original price of an orange and q = the original number of oranges purchased. We can create the equation for the original total cost:

pq = 12

q = 12/p

After the orange’s price is lowered, we have that 0.6p = the new (reduced) price of an orange and (q + 4) = the new number of oranges that can be purchased at the reduced price. Our new equation for total cost is:

(0.6p)(q + 4) = 12

0.6pq + 2.4p = 12

Substituting for q, we have:

0.6p(12/p) + 2.4p = 12

7.2 + 2.4p = 12

2.4p = 4.8

p = 2

That is, each orange is $2. So for $24, we can buy 24/2 = 12 oranges.

Answer: B
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Re: When the price of oranges is lowered by 40%, 4 more oranges   [#permalink] 04 Jul 2018, 19:25
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