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

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.

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

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 ....

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

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

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

Answer D.

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

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

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


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.

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.

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 = \(24-4 = 20\)

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..

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

Thanks for suggesting all approaches

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.

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

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:



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




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.