At the beginning of the day, the ratio of $5 bills to $10 bills in Th

Question

At the beginning of the day, the ratio of $5 bills to $10 bills in Thom’s wallet was 2 to 3. Thom then paid for a purchase with one $5 bill and four $10 bills, and did not receive change. Afterwards, Thom observed that the ratio of $5 bills to $10 bills in the wallet was 3 to 2. How many $5 bills were in Thom’s wallet at the beginning of the day?

(A) 4
(B) 6
(C) 8
(D) 10
(E) 12

(A) 4
(B) 6
(C) 8
(D) 10
(E) 12

GMATinsight · Answer

Total Money in beginning = 2x*5 + 3x*10 = 40x

Payment done = 5+10*4 = 45

(2x-1):(3x-4) = 3:2

i.e. 4x - 2= 9x - 12

i.e. 5x = 10

x = 2

i.e. 2x = 4

Answer: Option A

ScottTargetTestPrep · Answer

We can express the 2 : 3 ratio as 2x : 3x, where 2x is the number of $5 bills and 3x is the number of $10 bills. We can then create the equation:

(2x - 1) / (3x - 4) = 3/2

2(2x - 1) = 3(3x - 4)

4x - 2 = 9x - 12

10 = 5x

2 = x

Therefore, there were 2(2) = 4 $5 bills originally.

Answer: A

sushi600 · Answer

Question: How many 5 dollar bills were in Tom's wallet at the beginning of the day?

Given:
Ratio at the start of the day: 2:3. 
Ratio at the end of the day, after 1x5 dollar bill and 4x10 dollar bills are taken out, 3:2.

This question can be solved by plugging in the numbers from the answer choices.

Starting with B, 6, if there was at the start of the day 6 5 dollar bills, there would be 9 10 dollar bills. After taking out 1 5 dollar bill and 4 10 dollar bills, Tom would now be left with 5 5 dollar bills and 5 10 dollar bills. The new ratio would now be 5:5. This is not 3:2 therefore, it's wrong.

Now trying answer choices C, if there was at the start of the day 10 5 dollar bills, there would be 15 10 dollar bills. After taking out 1 5 dollar bill and 4 10 dollar bills, Tom would now be left with 5 9 dollar bills and 11 10 dollar bills. The new ratio would now be 9:11. This is not 3:2 therefore, it's wrong as well.

Since the answer choices are in an increasing order, we can see that the answer choice must be lower than 5:5 and lower than 9:11. Therefore we can pick answer choice A.

IanStewart · Answer

20% of the bills he spent were fives. 60% of the bills he kept at the end of the day were fives. Put together what he spent and what he kept, and you get back to what he started the day with, and at the start of the day, 40% of his bills were fives. This is now just a standard weighted average situation, and since 40% is halfway between 20% and 60%, the total number of bills he spent must be equal to the number he kept, so he had 5 bills left to end the day, and so had exactly 3 fives and 2 tens at the end of the day, and thus adding back what he spent, 4 fives and 6 tens at the start.

bumpbot · Answer

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At the beginning of the day, the ratio of $5 bills to $10 bills in Th

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