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Tourist purchased a total of 30 travelers checks in $50 and

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Re: Tourist purchased a total of 30 travelers checks in $50 and [#permalink]

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New post 05 Sep 2017, 18:04
Expert's post
GMATBaumgartner wrote:
Tourist purchased a total of 30 travelers checks in $50 and $100 denominations. The total worth of the travelers checks is $1800. How many checks of $50 denominations can he spend so that average amount (arithmetic mean) of the remaining travelers checks is $80?

A. 4
B. 12
C. 15
D. 20
E. 24


We can let x = the number of $50 traveler’s checks and y = the number of $100 traveler’s checks. Thus, we can create a “number of traveler’s checks” equation:

x + y = 30

x = 30 - y

We can also create a “monetary value” equation:

50x + 100y = 1800

We substitute (30 - y) for x:

50(30 - y) + 100y = 1800

1500 - 50y + 100y = 1800

50y = 300

y = 6

Since y = 6 and x = 30 - y, x = 24.

We can let n = the number of $50 traveler’s checks spent and create the following equation:

[50(24 - n) + 100(6)]/(30 - n) = 80

1200 - 50n + 600 = 2400 - 80n

30n = 600

n = 20

Answer: D
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Re: Tourist purchased a total of 30 travelers checks in $50 and [#permalink]

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New post 24 Sep 2017, 15:54
Solving Algebraically:

X = the number of checks in the $50 denominations
Y = the number of checks in the $100 denominations
Total number of checks = X + Y = 30

Total value of the checks = $50X + $100Y = $1800

let n = the number of $50 denomination checks the tourist spends

Calculate the average amount of the remaining checks:

=($1800 - $50n)/(X+Y-n) = $80
=($1800 - $50n)/(30- n) = $80
=$1800 - $50n = $80(30- n)
=$1800 - $50n = $2400 - $80n
=$30n = $600
n = 20
Answer: D
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GRE 1: 340 Q170 V170
Re: Tourist purchased a total of 30 travelers checks in $50 and [#permalink]

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New post 29 Nov 2017, 21:25
Expert's post
Hi All,

There are a couple of different ways to approach this question - depending on how you 'see' the math involved. This question can be solved rather quickly by TESTing THE ANSWERS.

From the prompt, we know that there are 30 checks in total (some are 50s and some are 100s) and the the SUM of their value is $1800. That means the 'starting average value' is 1800/30 = $60. As we remove 50s from that calculation, the average will INCREASE. The question asks how many of the 50s we have to remove to get the average up to $80.

Since $80 is a nice 'round number', it's likely that we'll end up removing a number of checks that will create a 'nice' number to divide by (such as a multiple of 5 or a multiple of 10). Looking at the answers, I would start with answer D, since removing 20 checks would leave us with 10 checks (and 10 will be easy to divide into whatever the new numerator is...

Let's TEST Answer D: 20

If we remove twenty 50s from the total value, then the new total value will be 1800 - (20)(50) = $800.
After removing those twenty checks, there will be 30 - 20 = 10 checks remaining.
The average of these remaining checks is $800/10 = $80
This matches what we were told, so this MUST be the answer.

Final Answer:
[Reveal] Spoiler:
D


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Expert Post
Target Test Prep Representative
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Re: Tourist purchased a total of 30 travelers checks in $50 and [#permalink]

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New post 04 Dec 2017, 11:37
Expert's post
GMATBaumgartner wrote:
Tourist purchased a total of 30 travelers checks in $50 and $100 denominations. The total worth of the travelers checks is $1800. How many checks of $50 denominations can he spend so that average amount (arithmetic mean) of the remaining travelers checks is $80?

A. 4
B. 12
C. 15
D. 20
E. 24


We can let a = the number of checks in 50-dollar denomination and b = the number of checks in 100-dollar denomination and create the equation:

50a + 100b = 1800

a + 2b = 36

We also know that a + b = 30.

Subtracting our second equation from our first, we have:

b = 6, so a = 24

We can let n = the number of 50-dollar checks to be spent and create the equation:

[50(24 - n) + 100(6)]/(30 - n) = 80

50(24 - n) + 100(6) = 80(30 - n)

5(24 - n) + 10(6) = 8(30 - n)

120 - 5n + 60 = 240 - 8n

3n = 60

n = 20

Answer: D
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Re: Tourist purchased a total of 30 travelers checks in $50 and   [#permalink] 04 Dec 2017, 11:37
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