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Re: Tom purchased a total of $5000 worth of travelers checks in $50 and $ [#permalink]
Expert Reply
Taking X as 50 denomination and Y as 100 denomination
We know total value will be 50X + 100Y
Value of Lost checks = 5000 - (50X+100Y) --- Eq 1
Taking X+Y=14, there will be two cases : X=Y+2 and X=Y-2
For 1st case we get X=8 and Y=6 and for 2nd case we get X=6 and Y=8

Putting these 2 cases in Eq1
We get
5000 - (1100) = 3900
or 5000 - (1000) = 4000
max value = 4000
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Re: Tom purchased a total of $5000 worth of travelers checks in $50 and $ [#permalink]
1
Step 1: Define Variables
Let x be the number of $50 checks cashed.
Let y be the number of $100 checks cashed.
Total number of checks cashed: x+y=14

Tom bought checks worth $5000, all in $50 and $100 denominations.
Step 2: Relationship between Cashed Checks
The problem says that the number of $50 checks cashed was two more or two less than the number of $100 checks cashed.
This gives us two possibilities:
i) x=y+2

ii) x=y−2

Step 3: Calculate Possible Values for

x and y
Case 1:
x=y+2

x+y=14
⟹(y+2)+y=14
⟹2y+2=14
⟹2y=12
⟹y=6,

x=y+2=6+2=8.

Cashed checks:
8 checks of $50 = =8×50=400
8×50=400
6 checks of $100 = 6×100=600

Total cashed value:
400+600=1000

Case 2:
x+y=14⟹(y−2)+y=14⟹2y−2=14⟹2y=16⟹y=8
So, x=y−2=8−2=6.

Cashed checks:
6 checks of $50 = 6×50=300

8 checks of $100 = 8×100=800

Total cashed value:

300+800=1100.

Step 4: Determine the Maximum Value Lost
Tom purchased checks worth $5000.

From the two cases, the total value of the checks cashed is either:

$1000 (from Case 1)
$1100 (from Case 2)
To maximize the value lost, we want the smallest amount cashed.

The smallest cashed amount is $1000 (from Case 1).
Value lost:


5000−1000=4000
Final Answer
The maximum possible value of checks lost is $4000.
Prep Club for GRE Bot
Re: Tom purchased a total of $5000 worth of travelers checks in $50 and $ [#permalink]
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