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

Question

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.

ID: 100437

sterling19 · Accepted Answer

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.

Sajjad1994 · Answer

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.

SlikRick · Answer

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.

raghaw · Answer

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.

SairamRamo · Answer

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

sameerm22 · Answer

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.

sanjitscorps18 · Answer

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

AnishPassi · Answer

Francois doesn't pay out $750.
Pierre doesn't pay out $250.
 
We have to select the figures that represent the total amounts these two owe, not what they have already paid.

Purnank · Answer

\frac{f}{2} + \frac{p}{10} = \frac{2(f+p)}{5}

After simplifying

f=3p

p=250  and  f=750

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