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22 Jan 2025, 01:30
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
70% (02:39) correct
30%
(02:48)
wrong
based on 155
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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?
A. $3800
B. $3900
C. $4000
D. $4100
E. None of the above
A. $3800
B. $3900
C. $4000
D. $4100
E. None of the above
Updated on: 22 Jan 2025, 02:48
Originally posted by bhargavhhhhhhhh on 22 Jan 2025, 02:47.
Last edited by bhargavhhhhhhhh on 22 Jan 2025, 02:48, edited 1 time in total.
Last edited by bhargavhhhhhhhh on 22 Jan 2025, 02:48, edited 1 time in total.
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Let x be the number of $50 checks cashed, and y be the number of $100 checks cashed.
We are told x = y ± 2 and x + y = 14.
Case 1: x = y + 2
Substitute x = y + 2 into x + y = 14:
(y + 2) + y = 14
2y + 2 = 14
2y = 12
y = 6, so x = 8.
The value of checks cashed = 50 * 8 + 100 * 6 = 1000.
The lost value = 5000 - 1000 = 4000.
Case 2: x = y - 2
Substitute x = y - 2 into x + y = 14:
(y - 2) + y = 14
2y - 2 = 14
2y = 16
y = 8, so x = 6.
The value of checks cashed = 50 * 6 + 100 * 8 = 1100.
The lost value = 5000 - 1100 = 3900.
The maximum value of the checks that were lost is $4000.
We are told x = y ± 2 and x + y = 14.
Case 1: x = y + 2
Substitute x = y + 2 into x + y = 14:
(y + 2) + y = 14
2y + 2 = 14
2y = 12
y = 6, so x = 8.
The value of checks cashed = 50 * 8 + 100 * 6 = 1000.
The lost value = 5000 - 1000 = 4000.
Case 2: x = y - 2
Substitute x = y - 2 into x + y = 14:
(y - 2) + y = 14
2y - 2 = 14
2y = 16
y = 8, so x = 6.
The value of checks cashed = 50 * 6 + 100 * 8 = 1100.
The lost value = 5000 - 1100 = 3900.
The maximum value of the checks that were lost is $4000.
22 Jan 2025, 02:48
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Lets say the no of \($50\) & \($100\) checks are \(a\) & \(b\)
\(a=b+2\) or \(a=b-2\)
cashed checks, \(a+b=14\)
when \(a=b+2\), \(2b+2=14\), \(b=6\), \(a=8\) & the cashed amount is \(600+400=$1000\)
when \(a=b-2\), \(2b-2=14\), \(b=8\), \(a=6\) & the cashed amount is \(800+300=$1100\)
The max amount of lost check will be \($5000-$1000=$4000\)
Answer: C
\(a=b+2\) or \(a=b-2\)
cashed checks, \(a+b=14\)
when \(a=b+2\), \(2b+2=14\), \(b=6\), \(a=8\) & the cashed amount is \(600+400=$1000\)
when \(a=b-2\), \(2b-2=14\), \(b=8\), \(a=6\) & the cashed amount is \(800+300=$1100\)
The max amount of lost check will be \($5000-$1000=$4000\)
Answer: C
