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A certain scholarship committee awarded scholarships in the [#permalink]

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24 Apr 2010, 16:07

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A certain scholarship committee awarded scholarships in the amounts of $1250, $2500 and $4000. The Committee awarded twice as many $2500 scholarships as $4000 and it awarded three times as many $1250 scholarships as $2500 scholarships. If the total of $37500 was awarded in $1250 scholarships, how many $4000 scholarships were awarded?

Re: How many scholarships were awarded? [#permalink]

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25 Apr 2010, 01:17

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zz0vlb wrote:

A certain scholarship committee awarded scholarships in the amounts of $1250,$2500 and $4000. The Committe awarded twice as many $2500 scholarships as $4000 and it awarded three times as many $1250 scholarships as $2500 scholarships. If the total of $37500 was awarded in $1250 scholarships, how many $4000 scholarships were awarded?

This is a ratio question. So first find out the ratio of all three scholarships awarded

$1250 : $2500 : $4000 = 6:2:1 How - let x be the number of scholarships of $4000, then number of scholarship of $2500 will be 2x (twice than the other). then $1250 scholarships will be 6x (thrice of $2500 scholarship) Ratio 6x:2x:x = 6:2:1

Now $37500 is the total amount of $1250 scholarship. Hence, total 30 If $1250 scholarship are 30 then $4000 scholarship are 5 (divide 30 by 6)

Re: How many scholarships were awarded? [#permalink]

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09 Nov 2012, 13:13

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Here is my approach Let X, Y and Z be numbers of awards for $1250, $2500 and $4000 . (X = 3Y; Y = 2Z ==> X:Y:Z = 1:1/3:1/6 We know from the stem that X = 30 ($37500/$1250). Thus Y = 10 (30/3) and Z = 5 (30/6) Brother Karamazov

Re: A certain scholarship committee awarded scholarships in the [#permalink]

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10 Nov 2012, 04:42

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Expert's post

zz0vlb wrote:

A certain scholarship committee awarded scholarships in the amounts of $1250, $2500 and $4000. The Committee awarded twice as many $2500 scholarships as $4000 and it awarded three times as many $1250 scholarships as $2500 scholarships. If the total of $37500 was awarded in $1250 scholarships, how many $4000 scholarships were awarded?

A. 5 B. 6 C. 9 D. 10 E. 15

Say the number of $4,000 scholarships awarded was x, then the number of $2,500 scholarships awarded would be 2x and the number of $1,250 scholarships awarded would be 6x.

Re: A certain scholarship committee awarded scholarships in the [#permalink]

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19 Jan 2014, 01:38

aiha85 wrote:

My answer was 180 because I switch numbers in the question then when I did not find 180 I said ok do the opposite, then I got the right answer.

these kind of phrases are killing me "twice as many $2500 scholarships as $4000" "three times as many $1250 scholarships as $2500"

which is which .. Can anyone give me the right way of figuring these kind of phrases out very quickly? LOOL

Yes, I'm also confused with the phrases (twice as many XXX as XXX). Remember we have a very similar question, that is, (see below)

"At a certain college there are twice as many English majors as history majors and three times as many English majors as mathematics majors. What is the ratio of the number of history majors to the number of mathematics majors?" The correct answer is 3:2 (rather than 2:3).

The expression is the same in these TWO questions, but why not the same understanding?

Re: A certain scholarship committee awarded scholarships in the [#permalink]

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19 Jan 2014, 09:34

Expert's post

smallapple wrote:

aiha85 wrote:

My answer was 180 because I switch numbers in the question then when I did not find 180 I said ok do the opposite, then I got the right answer.

these kind of phrases are killing me "twice as many $2500 scholarships as $4000" "three times as many $1250 scholarships as $2500"

which is which .. Can anyone give me the right way of figuring these kind of phrases out very quickly? LOOL

Yes, I'm also confused with the phrases (twice as many XXX as XXX). Remember we have a very similar question, that is, (see below)

"At a certain college there are twice as many English majors as history majors and three times as many English majors as mathematics majors. What is the ratio of the number of history majors to the number of mathematics majors?" The correct answer is 3:2 (rather than 2:3).

The expression is the same in these TWO questions, but why not the same understanding?

Who can help? Thank you.

Translation is the same for both questions.

Twice as many $2500 scholarships as $4000 means that if the number of $4000 scholarships was x, then the number of $2500 scholarships was 2x.

Three times as many $1250 scholarships as $2500 scholarships means that if the number of $2500 scholarships was 2x, then the number of $1250 scholarships was 3*(2x)=6x.

As for another question: At a certain college there are twice as many english majors as history majors and three times as many english majors as mathematics majors. What is the ratio of the number of history majors to the number of mathematics majors?

At a certain college there are twice as many english majors as history majors: E = 2H (as there are MORE english majors)

and three times as many english majors as mathematics majors: E = 3M (as there are MORE english majors)

What is the ratio of the number of history majors to the number of mathematics majors? What is \(\frac{H}{M}\)?

Re: A certain scholarship committee awarded scholarships in the [#permalink]

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20 Jan 2014, 04:54

Bunuel wrote:

smallapple wrote:

aiha85 wrote:

My answer was 180 because I switch numbers in the question then when I did not find 180 I said ok do the opposite, then I got the right answer.

these kind of phrases are killing me "twice as many $2500 scholarships as $4000" "three times as many $1250 scholarships as $2500"

which is which .. Can anyone give me the right way of figuring these kind of phrases out very quickly? LOOL

Yes, I'm also confused with the phrases (twice as many XXX as XXX). Remember we have a very similar question, that is, (see below)

"At a certain college there are twice as many English majors as history majors and three times as many English majors as mathematics majors. What is the ratio of the number of history majors to the number of mathematics majors?" The correct answer is 3:2 (rather than 2:3).

The expression is the same in these TWO questions, but why not the same understanding?

Who can help? Thank you.

Translation is the same for both questions.

Twice as many $2500 scholarships as $4000 means that if the number of $4000 scholarships was x, then the number of $2500 scholarships was 2x.

Three times as many $1250 scholarships as $2500 scholarships means that if the number of $2500 scholarships was 2x, then the number of $1250 scholarships was 3*(2x)=6x.

As for another question: At a certain college there are twice as many english majors as history majors and three times as many english majors as mathematics majors. What is the ratio of the number of history majors to the number of mathematics majors?

At a certain college there are twice as many english majors as history majors: E = 2H (as there are MORE english majors)

and three times as many english majors as mathematics majors: E = 3M (as there are MORE english majors)

What is the ratio of the number of history majors to the number of mathematics majors? What is \(\frac{H}{M}\)?

Re: A certain scholarship committee awarded scholarships in the [#permalink]

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08 Dec 2015, 00:46

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Re: A certain scholarship committee awarded scholarships in the [#permalink]

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08 Dec 2015, 23:40

Expert's post

Quote:

A certain scholarship committee awarded scholarships in the amounts of $1250, $2500 and $4000. The Committee awarded twice as many $2500 scholarships as $4000 and it awarded three times as many $1250 scholarships as $2500 scholarships. If the total of $37500 was awarded in $1250 scholarships, how many $4000 scholarships were awarded?

Since the starting point is given as the $4000 scholarship, Assume $4000 scholarships to be x By the given information, $2500 scholarships = 2x and $1250 scholarships = 6x

Gievn: Total $1250 scholarships = $37500 6x*1250 = 37500 Solve for x = 5 Option A _________________

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