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Tom purchased a total of $5000 worth of travelers checks in $50 and $
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19 Apr 2023, 08:39
19 Apr 2023, 08:39
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73% (02:59) correct
26% (04:01) wrong based on 15 sessions
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Tom purchased a total of $5000 worth of traveler’s checks in $50 and $100 denominations for his vacation. During his vacation Tom cashed 14 checks and then lost all the rest. If the number of $50 checks cashed was two more or two less than the number of $100 checks cashed, what is the maximum possible value of checks that were lost?
$3800
$3900
$4000
$4100
None of the above
$3800
$3900
$4000
$4100
None of the above
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Tom purchased a total of $5000 worth of travelers checks in $50 and $
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22 Apr 2023, 00:46
22 Apr 2023, 00:46
1
Expert Reply
Let x be the number of $50 traveler's checks Tom purchased, and y be the number of $100 traveler's checks he purchased. We know that:
x = y ± 2 (the number of $50 traveler's checks cashed is two more or two less than the number of $100 traveler's checks cashed)
We can solve for x and y by substituting the second equation into the first:
(y + 2) + y = 100 or (y - 2) + y = 100
Simplifying each equation gives 2y = 98 or 2y = 102, so y = 49 or y = 51
Plugging in these values for y gives x = 51 or x = 47
Tom cashed 14 checks, so we know that he cashed either 7 $50 checks and 7 $100 checks, or 8 $50 checks and 6 $100 checks.
If he cashed 7 $50 checks and 7 $100 checks, the total value of the checks he cashed is 7($50) + 7($100) = $1050.
If he cashed 8 $50 checks and 6 $100 checks, the total value of the checks he cashed is 8($50) + 6($100) = $1100.
The maximum possible value of the checks that were lost is the difference between the total value of all the traveler's checks purchased and the total value of the checks Tom cashed:
If he cashed 7 $50 checks and 7 $100 checks, the total value of all the traveler's checks purchased is 51($50) + 49($100) = $5050, so the maximum possible value of the checks that were lost is $5050 - $1050 = $4000.
If he cashed 8 $50 checks and 6 $100 checks, the total value of all the traveler's checks purchased is 47($50) + 51($100) = $5050, so the maximum possible value of the checks that were lost is $5050 - $1100 = $3950.
Therefore, the maximum possible value of checks that were lost is $4000, and the answer is (C) $4000.
x = y ± 2 (the number of $50 traveler's checks cashed is two more or two less than the number of $100 traveler's checks cashed)
We can solve for x and y by substituting the second equation into the first:
(y + 2) + y = 100 or (y - 2) + y = 100
Simplifying each equation gives 2y = 98 or 2y = 102, so y = 49 or y = 51
Plugging in these values for y gives x = 51 or x = 47
Tom cashed 14 checks, so we know that he cashed either 7 $50 checks and 7 $100 checks, or 8 $50 checks and 6 $100 checks.
If he cashed 7 $50 checks and 7 $100 checks, the total value of the checks he cashed is 7($50) + 7($100) = $1050.
If he cashed 8 $50 checks and 6 $100 checks, the total value of the checks he cashed is 8($50) + 6($100) = $1100.
The maximum possible value of the checks that were lost is the difference between the total value of all the traveler's checks purchased and the total value of the checks Tom cashed:
If he cashed 7 $50 checks and 7 $100 checks, the total value of all the traveler's checks purchased is 51($50) + 49($100) = $5050, so the maximum possible value of the checks that were lost is $5050 - $1050 = $4000.
If he cashed 8 $50 checks and 6 $100 checks, the total value of all the traveler's checks purchased is 47($50) + 51($100) = $5050, so the maximum possible value of the checks that were lost is $5050 - $1100 = $3950.
Therefore, the maximum possible value of checks that were lost is $4000, and the answer is (C) $4000.
Re: Tom purchased a total of $5000 worth of travelers checks in $50 and $
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15 Oct 2023, 05:56
15 Oct 2023, 05:56
1
GeminiHeat wrote:
Let x be the number of $50 traveler's checks Tom purchased, and y be the number of $100 traveler's checks he purchased. We know that:
x + y = 5000 / 50 = 100 (the total number of traveler's checks purchased)
x = y ± 2 (the number of $50 traveler's checks cashed is two more or two less than the number of $100 traveler's checks cashed)
We can solve for x and y by substituting the second equation into the first:
(y + 2) + y = 100 or (y - 2) + y = 100
Simplifying each equation gives 2y = 98 or 2y = 102, so y = 49 or y = 51
Plugging in these values for y gives x = 51 or x = 47
Tom cashed 14 checks, so we know that he cashed either 7 $50 checks and 7 $100 checks, or 8 $50 checks and 6 $100 checks.
If he cashed 7 $50 checks and 7 $100 checks, the total value of the checks he cashed is 7($50) + 7($100) = $1050.
If he cashed 8 $50 checks and 6 $100 checks, the total value of the checks he cashed is 8($50) + 6($100) = $1100.
The maximum possible value of the checks that were lost is the difference between the total value of all the traveler's checks purchased and the total value of the checks Tom cashed:
If he cashed 7 $50 checks and 7 $100 checks, the total value of all the traveler's checks purchased is 51($50) + 49($100) = $5050, so the maximum possible value of the checks that were lost is $5050 - $1050 = $4000.
If he cashed 8 $50 checks and 6 $100 checks, the total value of all the traveler's checks purchased is 47($50) + 51($100) = $5050, so the maximum possible value of the checks that were lost is $5050 - $1100 = $3950.
Therefore, the maximum possible value of checks that were lost is $4000, and the answer is (C) $4000.
x + y = 5000 / 50 = 100 (the total number of traveler's checks purchased)
x = y ± 2 (the number of $50 traveler's checks cashed is two more or two less than the number of $100 traveler's checks cashed)
We can solve for x and y by substituting the second equation into the first:
(y + 2) + y = 100 or (y - 2) + y = 100
Simplifying each equation gives 2y = 98 or 2y = 102, so y = 49 or y = 51
Plugging in these values for y gives x = 51 or x = 47
Tom cashed 14 checks, so we know that he cashed either 7 $50 checks and 7 $100 checks, or 8 $50 checks and 6 $100 checks.
If he cashed 7 $50 checks and 7 $100 checks, the total value of the checks he cashed is 7($50) + 7($100) = $1050.
If he cashed 8 $50 checks and 6 $100 checks, the total value of the checks he cashed is 8($50) + 6($100) = $1100.
The maximum possible value of the checks that were lost is the difference between the total value of all the traveler's checks purchased and the total value of the checks Tom cashed:
If he cashed 7 $50 checks and 7 $100 checks, the total value of all the traveler's checks purchased is 51($50) + 49($100) = $5050, so the maximum possible value of the checks that were lost is $5050 - $1050 = $4000.
If he cashed 8 $50 checks and 6 $100 checks, the total value of all the traveler's checks purchased is 47($50) + 51($100) = $5050, so the maximum possible value of the checks that were lost is $5050 - $1100 = $3950.
Therefore, the maximum possible value of checks that were lost is $4000, and the answer is (C) $4000.
Sir, I think x + y = 5000/ 50 is incorrect since there is nothing in the question to suggest that a total of 50 checks were issued
