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Francois and Pierre each owe Claudine money. Today, Francois will make

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sinsve
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Francois and Pierre each owe Claudine money. Today, Francois will make [#permalink] New post   Updated on: 29 Sep 2023, 12:08
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Francois and Pierre each owe Claudine money. Today, Francois will make a payment equal to 50% of the amount he owes Claudine, and Pierre will make a payment equal to 10% of the amount he owes Claudine. Together, the two payments will be equal to 40% of the combined amount that Francois and Pierre owe Claudine.

Select for Francois and Pierre amounts that Francois and Pierre could owe Claudine that are jointly consistent with the given information. Make only two selections, one in each column.
Francois Pierre
€50
€250
€750
€3,750
€6,750
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Official Answer
Francois: €750 Pierre: €250

Originally posted by sinsve on 20 Feb 2015, 10:53.
Last edited by BottomJee on 29 Sep 2023, 12:08, edited 5 times in total.
Updated - Complete topic (115).
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Re: Francois and Pierre each owe Claudine money. Today, Francois will make [#permalink] New post   20 Feb 2015, 12:54
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You did this correctly. If Francois = F and Pierre = P, then...

\(.5F + .1P = .4(F+P)\)

\(.5F + .1P = .4F + .4P\)

\(.1F = .3P\) or \(F = 3P\)

You must select the right combination of answer choices that make this statement true.
Only €750 and €250 make this possible.
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Re: Francois and Pierre each owe Claudine money. Today, Francois will make [#permalink] New post   15 Sep 2021, 09:30
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Official Explanation

If the amounts, in euros (€), that Francois and Pierre owe Claudine are €x and €y, respectively, then Francois’s payment was €0.50(x), Pierre’s payment was €0.10(y), and the combined amount that Francois and Pierre owe Claudine is €(x + y). We are given that the sum of their payments will be equal to 40% of this combined amount. Therefore 0.50x + 0.10y = 0.40(x + y). Combining like terms gives us x = 3y, so Francois must owe Claudine exactly three times the amount Pierre owes her. Among the available options, there is only one pair of options (€250 and €750) for which the larger value in the pair is 3 times the smaller value.
Since Francois owes the larger of the two amounts, Francois must owe €750.

The correct answer is €750.

Since Pierre owes the smaller of the two amounts, Pierre must owe €250.

The correct answer is €250.
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Re: Francois and Pierre each owe Claudine money. Today, Francois will make [#permalink] New post   03 Jan 2017, 17:30
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Here's what I'm not understanding...

If Francois pays out $750, then he owes $1,500. ($750 is 50% of $1,500).
If Pierre pays out $250, then he owes $2,500. ($250 is 10% of $2,500).

Together, Francois and Pierre pay out a total of $1,000. However, they owe Claudine a total of $4,000 ($1,500 + $2,500). $1,000 is not 40% of $4,000.

Now, if you use $750 for Francois and only $50 for Pierre, the math works out as follows:

Total Payment = 750 + 50 = 800
Total Owed = 1500 + 500 = 2000

And $800 is 40% of $2,000.

Could someone PLEASE shed some light. I've been tinkering over this problem for the past hour. :(
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Re: Francois and Pierre each owe Claudine money. Today, Francois will make [#permalink] New post   04 Feb 2017, 12:59
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0.5 F + 0.1 P = 0.4 (F + P)
If F owes 750 then he pays 750*0.5 = 375
if P owes 250 then he pays 250*0.1 = 25
Total = 375 + 25 = 400
Now 40 % of combined= 0.4 * (750 + 250) = 400
Both are same.
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Re: Francois and Pierre each owe Claudine money. Today, Francois will make [#permalink] New post   27 Jul 2020, 07:35
Let X be the total amount Francois owes and Y be the total amount Pierre owes

given 0.5X + 0.1Y = 0.4(X+Y) -> X=3Y

Now comes the tricky part, The ask from the question can be interpreted in 2 ways

1) The Remaining amount they owe after the above payment (i.e 0.5X, 0.9Y)

Ratio of the owed amounts(Francois : Pierre)= 0.5x : 0.9y = 1.5y : 0.9y = 5: 3

None of the combinations in the given choices satisfy the above ratio

OR

2) The actual owed amount before paying the 1st installment (i.e X, Y)

Ratio of the owed amounts(Francois : Pierre)= x : 0.9 = 3y : y = 3: 1

Francois : Pierre = 750 : 250 satisify the above ratio


Personally I feel the ask from the question should have been more precise.

When i solved this question in the practice mock, I went with approach 1. So got it wrong in then
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Re: Francois and Pierre each owe Claudine money. Today, Francois will make [#permalink] New post   10 Sep 2020, 18:16
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This can be done under a minute using weighted average method. Thanks to VeritasKarishma.
Setting up weights for P and F,

P (10%) ----------------------- Avg (40%) ----------------------- F(50%)

By this we know that P/F = 10/30 = 1/3. So, you just need to pick answer choices that are consistent with F=3P.
So, choice B for P, and choice C for F.
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Re: Francois and Pierre each owe Claudine money. Today, Francois will make [#permalink] New post   15 Sep 2021, 23:14
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SlikRick wrote:
Here's what I'm not understanding...

If Francois pays out $750, then he owes $1,500. ($750 is 50% of $1,500).
If Pierre pays out $250, then he owes $2,500. ($250 is 10% of $2,500).

Together, Francois and Pierre pay out a total of $1,000. However, they owe Claudine a total of $4,000 ($1,500 + $2,500). $1,000 is not 40% of $4,000.

Now, if you use $750 for Francois and only $50 for Pierre, the math works out as follows:

Total Payment = 750 + 50 = 800
Total Owed = 1500 + 500 = 2000

And $800 is 40% of $2,000.

Could someone PLEASE shed some light. I've been tinkering over this problem for the past hour. :(


Originally, F owed $750 and P owed $250

F paid back $375 (50%) an P paid back $25 (10%)

Total amount originally owed = $750 + $250 = $1000
Total paid back = $375 + $25 = $400

$400 is 40% of $1000

Hope this helps
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Re: Francois and Pierre each owe Claudine money. Today, Francois will make [#permalink] New post   13 Feb 2024, 06:06
Expert Reply
SlikRick wrote:
Here's what I'm not understanding...

If Francois pays out $750, then he owes $1,500. ($750 is 50% of $1,500).
If Pierre pays out $250, then he owes $2,500. ($250 is 10% of $2,500).

Together, Francois and Pierre pay out a total of $1,000. However, they owe Claudine a total of $4,000 ($1,500 + $2,500). $1,000 is not 40% of $4,000.

Now, if you use $750 for Francois and only $50 for Pierre, the math works out as follows:

Total Payment = 750 + 50 = 800
Total Owed = 1500 + 500 = 2000

And $800 is 40% of $2,000.

:(



Francois doesn't pay out $750.
Pierre doesn't pay out $250.
Quote:
Select for Francois and Pierre amounts that Francois and Pierre could owe Claudine­

We have to select the figures that represent the total amounts these two owe, not what they have already paid.
 
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Re: Francois and Pierre each owe Claudine money. Today, Francois will make [#permalink]
13 Feb 2024, 06:06
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