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# The number of stamps that Kaye and Alberto had were in the

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Re: The number of stamps that Kaye and Alberto had were in the  [#permalink]

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11 Oct 2016, 08:35
kilukilam wrote:
The number of stamps that Kaye and Alberto had were in the ration of 5:3 respecctively. After Kaye gave Alberto 10 of her stamps, the ration of the number of Kaye had to the number of Alberto had was 7:5. As a result of the gift, Kaye had how many more stamps than Alberto

A. 20
B. 30
C. 40
D. 60
E. 90

Lets work -
Quote:
The number of stamps that Kaye and Alberto had were in the ration of 5:3 respectively.

Attachment:

1.PNG [ 1.09 KiB | Viewed 1150 times ]

Quote:
After Kaye gave Alberto 10 of her stamps, the ration of the number of Kaye had to the number of Alberto had was 7:5.

Attachment:

2.PNG [ 1.48 KiB | Viewed 1148 times ]

So, $$\frac{(5x-10)}{(3x+10)} = \frac{7}{5}$$

Or, $$25x - 50 = 21x + 70$$

Or, $$4x = 120$$

Or, $$x = 30$$

We are asked to find -
Quote:
As a result of the gift, Kaye had how many more stamps than Alberto

Or, (5x-10) - (3x+10) => 2x - 20

Or, 2(30) - 20 =40

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Re: The number of stamps that Kaye and Alberto had were in the  [#permalink]

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11 Oct 2016, 14:37
The number of stamps that Kaye and Alberto had were in the ratio of 5:3 respectively. After Kaye gave Alberto 10 of her stamps,
the ratio of the number Kaye had to the number Alberto had was 7:5. As a result of the gift, Kaye had how many more stamps than Alberto?

A. 20
B. 30
C. 40
D. 60
E. 90

let x=total stamps
5/8*x-10=7/12*x
x=240
7/12*240=140
5/12*240=100
140-100=40
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Re: The number of stamps that Kaye and Alberto had were in the  [#permalink]

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11 Oct 2016, 15:01
kilukilam wrote:
The number of stamps that Kaye and Alberto had were in the ration of 5:3 respecctively. After Kaye gave Alberto 10 of her stamps, the ration of the number of Kaye had to the number of Alberto had was 7:5. As a result of the gift, Kaye had how many more stamps than Alberto

A. 20
B. 30
C. 40
D. 60
E. 90

We are given that the number of stamps that Kaye and Alberto had were in the ratio 5 : 3. We can represent this as:

K : A = 5x : 3x

We are next given that after Kaye gave Alberto 10 of her stamps, the ratio of the number Kaye had to the number Alberto had was 7 : 5. Using this information we can create the following equation:

(5x – 10)/(3x + 10)= 7/5

5(5x – 10) = 7(3x + 10)

25x – 50 = 21x + 70

4x = 120

x = 30

Kaye now has 5(30) – 10 = 140 stamps and Alberto has 3(30) + 10 = 100 stamps. So Kaye has 140 – 100 = 40 more stamps than Alberto.

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Re: The number of stamps that Kaye and Alberto had were in the  [#permalink]

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28 Mar 2017, 12:44
this is a very very very! tricky question,
to avoid the trick I advise to write down from the beginning what the question asks, and this is: (5x-10)-(3x+10)

let's make up an equation:
(5x-10)/(3x+10)=7/5
we will find that x=30
Let's put it into the required formula above: (5*30-10)-(3*30+10)=40
be careful not to use ration 7:5, because it has no relation to x
this is where the whole trick is

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Re: The number of stamps that Kaye and Alberto had were in the  [#permalink]

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11 May 2017, 04:16
The number of stamps that Kaye and Alberto had were in the ration of 5:3 respecctively. After Kaye gave Alberto 10 of her stamps, the ration of the number of Kaye had to the number of Alberto had was 7:5. As a result of the gift, Kaye had how many more stamps than Alberto

A. 20
B. 30
C. 40
D. 60
E. 90

Solution: Let Kaye has 5x stamps and Alberto has 3x stamps. (5x:3x = 5:3)
When Kaye gives 10 stamps, he is left with (5x - 10) stamps.
and because Alebrto gets 10 stamps, he now has (3x + 10) stamps.
The new ratio is given as 7:5
=> (5x - 10)/((3x + 10) = 7/5
=> 5*(5x - 10) = 7*(3x + 10)
=> 25x - 50 = 21x + 70
=> 25x - 21x = 70 + 50
=> 4x = 120
=> x = 30
Don't be tempted to mark this as your answer. The question is asking something different. The question wants you to find the value of (5x - 10) - (3x + 10)

(5x - 10) - (3x + 10) = 2x - 20 = (2*30) - 20 = 60 - 20 = 40

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Re: The number of stamps that Kaye and Alberto had were in the  [#permalink]

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24 Jun 2017, 20:09
kilukilam wrote:
The number of stamps that Kaye and Alberto had were in the ration of 5:3 respecctively. After Kaye gave Alberto 10 of her stamps, the ration of the number of Kaye had to the number of Alberto had was 7:5. As a result of the gift, Kaye had how many more stamps than Alberto

A. 20
B. 30
C. 40
D. 60
E. 90

(5x - 10 )/ (3x + 10) = 7x/5x

(5x - 10)*5 = 7(3x+10)

25x - 50 = 21x + 70
4x = 120
x = 30

Now we need to find the final values after the trade occurs.

K: 5(30) - 10 = 150-10 = 140

A: 3(30) + 10 = 100

140 - 100 = 40.
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Re: The number of stamps that Kaye and Alberto had were in the  [#permalink]

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24 Jul 2017, 04:59
Bunuel, could you explain whats wrong with the the following method?

x/y =3/5. x-10/y+10 = 7/5. Hence on solving we get x as 50 and y as 30, which clearly does not tell us the answer. Can you please provide some conceptual clarity?
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Re: The number of stamps that Kaye and Alberto had were in the  [#permalink]

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24 Jul 2017, 05:15
kilukilam wrote:
The number of stamps that Kaye and Alberto had were in the ration of 5:3 respecctively. After Kaye gave Alberto 10 of her stamps, the ration of the number of Kaye had to the number of Alberto had was 7:5. As a result of the gift, Kaye had how many more stamps than Alberto

A. 20
B. 30
C. 40
D. 60
E. 90

$$\frac{K}{A} = \frac{5x}{3x}$$

$$\frac{5x-10}{3x+10} = \frac{7}{5}$$

$$25x - 50 = 21x + 70$$
$$4x = 120$$
$$x = 30$$

$$A = 3(30)+10 = 100$$
$$K = 5(30)-10 = 140$$

$$K-A = 40$$. Ans - C.
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Re: The number of stamps that Kaye and Alberto had were in the  [#permalink]

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24 Jul 2017, 05:28
1
OreoShake wrote:
Bunuel, could you explain whats wrong with the the following method?

x/y =3/5. x-10/y+10 = 7/5. Hence on solving we get x as 50 and y as 30, which clearly does not tell us the answer. Can you please provide some conceptual clarity?

Hi, there are a couple of things to note here.

I'm assuming that you assigned the variables x and y as: Alberto = x, Kaye = y. First off, when two things are in a ratio they must be represented using a common variable, if there were no relationship mentioned, for instance if it says that Kaye and Alberto had some stamps, then you may assign two separate variables to each since we don't know in what way they are related, if at all.

Secondly, Kaye gave Alberto 10 stamps, so it must be x+10/y-10 = 7/5. This equation cannot be solved for x and y, one value has to be represented using the other, since there are 2 variables involved.
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Re: The number of stamps that Kaye and Alberto had were in the  [#permalink]

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06 Apr 2018, 07:52
kilukilam wrote:
The number of stamps that Kaye and Alberto had were in the ration of 5:3 respecctively. After Kaye gave Alberto 10 of her stamps, the ration of the number of Kaye had to the number of Alberto had was 7:5. As a result of the gift, Kaye had how many more stamps than Alberto

A. 20
B. 30
C. 40
D. 60
E. 90

We are given that the number of stamps that Kaye and Alberto had was in the ratio 5 : 3. We can represent this as:

K : A = 5x : 3x

We are next given that after Kaye gave Alberto 10 of her stamps, the ratio of the number Kaye had to the number Alberto had was 7 : 5. Using this information, we can create the following equation:

(5x – 10)/(3x + 10) = 7/5

5(5x – 10) = 7(3x + 10)

25x – 50 = 21x + 70

4x = 120

x = 30

Kaye now has 5(30) – 10 = 140 stamps, and Alberto has 3(30) + 10 = 100 stamps. So Kaye has 140 – 100 = 40 more stamps than Alberto has.

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Re: The number of stamps Kaye and Alberto had were in the ratio  [#permalink]

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15 Sep 2018, 13:44
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Re: The number of stamps Kaye and Alberto had were in the ratio &nbs [#permalink] 15 Sep 2018, 13:44

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