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The ratio of oranges to apples in a fruit basket is 3 to 4. However,

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The ratio of oranges to apples in a fruit basket is 3 to 4. However,  [#permalink]

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New post 15 Sep 2016, 04:07
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A
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Question Stats:

84% (01:24) correct 16% (01:36) wrong based on 175 sessions

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The ratio of oranges to apples in a fruit basket is 3 to 4. However, after Mary and Alan eat four apples, the ratio changes to 3 to 2. How many oranges are there in the fruit basket?

A. 2
B. 3
C. 6
D. 9
E. 12

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Re: The ratio of oranges to apples in a fruit basket is 3 to 4. However,  [#permalink]

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New post 15 Sep 2016, 05:00
Bunuel wrote:
The ratio of oranges to apples in a fruit basket is 3 to 4. However, after Mary and Alan eat four apples, the ratio changes to 3 to 2. How many oranges are there in the fruit basket?

A. 2
B. 3
C. 6
D. 9
E. 12


O / A = 3/4 => O = 3/4(A).

Now O/A-4 = 3/2 . Now sub O value in this...we get 3A / 4A-16 = 3/2 => A = 8 and O = 6.

IMO option C.
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Re: The ratio of oranges to apples in a fruit basket is 3 to 4. However,  [#permalink]

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New post 15 Sep 2016, 05:38
o a
3x 4x
3x 3
4x-4 2
=
6x = 12x-12
x = 2
3x = 6

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Re: The ratio of oranges to apples in a fruit basket is 3 to 4. However,  [#permalink]

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New post 15 Sep 2016, 14:39
Top Contributor
2
Bunuel wrote:
The ratio of oranges to apples in a fruit basket is 3 to 4. However, after Mary and Alan eat four apples, the ratio changes to 3 to 2. How many oranges are there in the fruit basket?

A. 2
B. 3
C. 6
D. 9
E. 12


Let O = # of oranges originally in basket
Let A = # of apples originally in basket

The ratio of oranges to apples in a fruit basket is 3 to 4
So, O/A = 3/4
Cross multiply to get: 4O = 3A

After Mary and Alan eat four apples, the ratio changes to 3 to 2
NOTE: I'm assuming they eat a TOTAL of 4 apples, and not 4 apples each.
So, the number of apples is now A - 4
So, the oranges to apples ratio is as follows: O/(A-4) = 3/2
Cross multiply to get: 2O = 3(A - 4)
Expand: 2O = 3A - 12

We now have the following system:
4O = 3A
2O = 3A - 12

SUBTRACT the bottom equation from the top equation to get: 2O = 12
Solve: O= 6

Answer:

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Re: The ratio of oranges to apples in a fruit basket is 3 to 4. However,  [#permalink]

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New post 15 Sep 2016, 14:51
1
1
Bunuel wrote:
The ratio of oranges to apples in a fruit basket is 3 to 4. However, after Mary and Alan eat four apples, the ratio changes to 3 to 2. How many oranges are there in the fruit basket?

A. 2
B. 3
C. 6
D. 9
E. 12


I vote for plugging in the answer choices on this one.

You can eliminate (A) immediately, since it's not a multiple of 3.

(B): if there are 3 oranges, there are 4 apples. After Mary and Alan eat 4 apples, there would be 0 apples. That's not a 3:2 ratio. Wrong.

(C): If there are 6 oranges, there are 8 apples. After Mary and Alan eat 4 apples, there would be 4 apples. That's 6:4, which is 3:2. Correct.
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Re: The ratio of oranges to apples in a fruit basket is 3 to 4. However,  [#permalink]

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New post 15 Sep 2016, 17:20
I thought a decrease of 2 units mean 4 apples. So one unit means 2 apples. Hence, 3 units of oranges mean 6 oranges :)


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Re: The ratio of oranges to apples in a fruit basket is 3 to 4. However,  [#permalink]

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New post 27 Oct 2016, 20:35
1
orange/apple = 3x/(4x-4) = 3/2
6x=12x-12
12=6x
x=2

3(2) = 6 oranges
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Re: The ratio of oranges to apples in a fruit basket is 3 to 4. However,  [#permalink]

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New post 05 Jan 2018, 00:05
Org:app::3:4;. Org:app-4::3:2
3/4APP: APP-4::3:2=3/2app=3(app-4)
12=3/2app=app is 8 org = 6

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Re: The ratio of oranges to apples in a fruit basket is 3 to 4. However, &nbs [#permalink] 05 Jan 2018, 00:05
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