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

Question

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

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

subhashghosh · Accepted Answer

X + y = 30
50x + 100y = 1800
=> X +2y = 36
=> Y = 6 x = 24
Let n be the number
So ((24-n) * 50 + 6*100)/(30-n) = 80

=> 120 – 5n + 60 = 240 -8n
=> 3n = 60
=> n = 20

Answer - D

mayer87 · Answer

actually there is no need to calculate the numbers of two checks. Here is how I got the correct answer:
 
say the number of checks need to be spent to get the final average amount of $80 is x
Average amount= amount of $100 checks / numbers of remaining checks

then 1800-50*x / 30-x =80
x= 20

Capricorn369 · Answer

This one took me 2+ min.

x+y = 30
50x+100y=1800
Solving both the equation will give you - x = 24 and y = 6.
Now one can start plug-n-play and can figure out that D fits the answer.
x=4, y=6 makes the average amount of the remaining travelers checks to $80.

D wins.

premnath · Answer

This can be solved easily using algorithm,
x + y = 30 ---(i)
50x +100y=1800
=> x+2y=36 ---- (ii)

Therefore from equation (i) and (ii) we get, y=6 
Let, we can use the algorithm to find how 50 and 100 make the average to 80

................50......................100
............................80
...........(100-80)...............(80-50)
..............=20......................=30
>> ............2 .........................3 (this is the ratio by which 50 & 100 are to be combined to make average of 80)
>> .............4.........................6 (just multiplying both sides with 2, it does not change the ratio)

This means if we have six 100 and four 50 we will get average 80 considering all notes
So, extra 50 notes are 24-4= 20

Bunuel · Answer

Similar question to practice: a-tourist-purchased-a-total-of-1-500-worth-of-traveler-s-111369.html

shelrod007 · Answer

I am confused as to why cant we do the opposite for this

(24*50 + (6-n)*100)/(30-n)) = 80 ? 
The answer doesnt hold then ....

avohden · Answer

you could set-up a quick table and brute force the answer.

A 4 * 50 200 1800 -200 1600 26 61.54 
B 12 * 50 600 1800 -600 1200 18 66.67 
C 15 * 50 750 1800 -750 1050 15 70.00 
D 20 * 50 1000 1800 -1000 800 10 80.00 
E 24 * 50 1200 1800 -1200 600 6 100.00

unceldolan · Answer

average is 80 $, only pssible total amount for this is 800 $. Hence he can spend 1000 $ which equals to 20 50$ checks.

Answer D.

AliciaSierra · Answer

I took more than 2min to solve this question.  Is there any quick way? 
 My approach was this.

Initially, Tourist had total 30 travelers checks.
Let say say, he initially had x number of $50 travelers checks. So he will have 30-x number of $100 travelers checks.
The total worth of the travelers checks is $1800.

x*50 + (30-x)*100 = 1800
x*5+(30-x)*10=180
300-x*5=180
x=24

So he had 24 fifty dollar travelers checks and (30-24=6) hundred dollar travelers checks.

Suppose he spends few checks, remaining number of $50 is y

(5*y+6*100)/(y+6) = 80 ----comments:- Weight Average Mean Formula. He did not spend any $100 checks so 6 is as it is. 
y=4

he was left with only 4 checks of $50. So he spent 20 checks of $ 50.

Answer is D

reto · Answer

I Also had 2+ minutes until i figured out, that it might be the best way to start plugging in. Start in the middle with plugging in and check if the answer fits the average ov $80.
Start Plugging in 15 and you get 15*50 = 750 spent leaving 1050 USD and 15 tickets averaging $70 > eliminate this answer choice. If youre not sure which way to go, choose one direction, plug in 20 and you get 20*50 = 1000 spent leaving 800 USD and 20 tickets averaging $80.

Very easy, but it took me more than 5min to figure out which method to take ... poor me

korrag · Answer

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

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

let x be the number of $50 checks he had to start with.
50x + 100(30-x) = 1800
Solving, we get x=24

therefore he had 6 $100 checks (value $600)

After he spends some $50 checks, let y be the total number of checks he has remaining.
Therefore,
80y = 6*100 + 50(y-6) ....... eqauting the value of the checks
we get y=10
Hence we had 10 total checks remaining, out of which 6 were $100 and 4 $50.
Therefore, he spend 20 $50 checks.

Divyadisha · Answer

It took me more than 2 mins.

x+y= 30
50x +100y= 1800

Solving the above equation we get x= 24, y=6

Suppose the person can spend 'n' $50 checks, then the equation becomes

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

Solving the equation we get 'n'= 20

chetan2u , please advise if there is any shortcut method for it.

chetan2u · Answer

Hi,
after you have got x= 24 and y=6, you can use weighted average method to find the rest of the answer..
for average of 80, the ratio of # of 50 and # of 100 =  \frac{100-80}{80-50} = \frac{2}{3} ..
therefore you should have 2 * 50$ for every 3 *100$...
but we have 6 *100$, so # of 50$ =  2 *\frac{6}{3}= 4 ..
and he can spend the REST =  24-4 = 20

chetan2u · Answer

Two more methods would be -
1)substitute - 
you can substitute one by one and find...
2) Logic..
# of 50 is 24 and # of 100 is 6....
so if both are 6, the average is 75$, but we are looking for higher average, 80$, so # of 50 $ has to be less than 6... ONLY 24 - 20 =4 fits in..

gracie · Answer

equation 1: 50x+100y=1800
equation 2: 50(x-z)+100y=80(30-z)➡
50x+100y=2400-30z
therefore,
1800=2400-30z
z=20 $50 checks he needs to spend

Divyadisha · Answer

Thanks for suggesting all approaches :thanks

saiesta · Answer

Took me almost 3 min. but only because I figured out after 2 min. that the best method to solve this question is by plugging in the numbers.

PK32 · Answer

Let the Number of $50 that we can spend be X.

Then, 1800- 50X/30-X = 80

We can solve for X and the answer will be X= 20

Option D

adiagr · Answer

I present an alternate and fast method to do such problems. These are essentially "mixture" problems and can be done by using alligation approach. Refer following figure: Moneybill-1.JPG Total checks are 30. Total value is 1800. This means average value is (1800/30) = 60. Once we have individual values, we can get the ratios. We find that 100$ checks and 50$ checks are in the ratio of 1:4. say 100$ checks are x in no. then 50$ checks are 4x in number x+4x = 30, so 5x = 30; x = 6. 100$ --> 6 in Number 50$--> 24 in Number Now let us come to second part. Refer following figure Moneybill-2.JPG Revised average = 80 We find that 100$ checks and 50$ checks are in the ratio of 3:2 Now we know that 100$ checks are 6 in number. 3: 2 is same is 6:4. hence 50$ checks will have to be 4 in Number. Originally 50$ checks were 24 in number. So 20 checks will be given away. D is the answer.

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

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

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