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Michael cashed a check for $1,200 and received only $10 and $50 bills

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Bunuel
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Michael cashed a check for $1,200 and received only $10 and $50 bills [#permalink] Michael cashed a check for $1,200 and received only $10 and $50 bills   13 Jan 2024, 03:30
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Michael cashed a check for $1,200 and received only $10 and $50 bills in return. During the course of a day, he used 15 bills and then lost the rest of the money. If the number of $10 bills used was either one more or one less than the number of $50 bills used, what is the minimum possible amount of money that was lost?

(A) $830
(B) $800
(C) $770
(D) $730
(E) $700
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D
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Re: Michael cashed a check for $1,200 and received only $10 and $50 bills [#permalink] Michael cashed a check for $1,200 and received only $10 and $50 bills   13 Jan 2024, 05:30
Bunuel
Michael cashed a check for $1,200 and received only $10 and $50 bills in return. During the course of a day, he used 15 bills and then lost the rest of the money. If the number of $10 bills used was either one more or one less than the number of $50 bills used, what is the minimum possible amount of money that was lost?

(A) $830
(B) $800
(C) $770
(D) $730
(E) $700

OA is D

Total 15 bills used, As per question below scenario can happen :

Case 1 - 10$ - 8 50$ - 7 Total = 430$ Lost = 1200-430 = 770$
Case 2 - 10$ - 7 50$ - 8 Total = 470$ Lost = 1200-470 = 730$
Minimum lost - 730$
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Michael cashed a check for $1,200 and received only $10 and $50 bills [#permalink] Michael cashed a check for $1,200 and received only $10 and $50 bills   19 Jan 2024, 11:06
Bunuel
Michael cashed a check for $1,200 and received only $10 and $50 bills in return. During the course of a day, he used 15 bills and then lost the rest of the money. If the number of $10 bills used was either one more or one less than the number of $50 bills used, what is the minimum possible amount of money that was lost?

(A) $830
(B) $800
(C) $770
(D) $730
(E) $700

If x is the amount of 10$ bills. And y was the amount of 50$ bills.
We have: 10x + 50y = 1200

We are looking for the minimum possible amount that was lost, therefore the amount of the 15 bills that were spent has to be maximum.
Thus we are looking for 10x + 50y that is max, where x + y = 15
From the prompt, x can either be y - 1 or y + 1
For 10x + 50y to be max y has to be the biggest factor between ( y ; x) therefore x is y - 1
So ( y ; x) = ( 8 ; 7)

Amount that was used: 10*7 + 50*8 = 470
Amount that was lost: 1200 - 470 = 730 (D)

If anyone has a quicker way of solving this and explaining how 8 and 7 are the factors that maximise 10x + 50y please advise :)
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Re: Michael cashed a check for $1,200 and received only $10 and $50 bills [#permalink] Michael cashed a check for $1,200 and received only $10 and $50 bills   20 Sep 2024, 23:44
Assuming no. of 50 bills as x.
No of 10 bills are x+1 or x-1
2x+1=15 => x=7
2x-1=15=> x=8
Minimum lost =>so maximum used.
Max used when there is more 50 bills out of 15.
So x=8
Then money lost = 1200 - money used = 1200-(8*50+7*10)=1200-470=730
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Re: Michael cashed a check for $1,200 and received only $10 and $50 bills [#permalink]
20 Sep 2024, 23:44
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Bunuel
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