Solving Don's Birthday Gift Puzzle

  • Thread starter K Sengupta
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In summary: I'll make sure to not use it in the future. In summary, Albert, Bob, and Cal pooled their money to buy Don a birthday present, spending a total of $5.50. Albert spent 50 cents more than 1/4 of the total amount, Bob spent a dollar more than half of what was left after Albert's purchase, and Cal spent $1.50 more than 3/4 of what was left. They ended up sharing a Big Mac, medium fries, and a medium drink with the remaining $5.50.
  • #1
K Sengupta
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Albert, Bob and Cal each gave a birthday gift to their friend Don, who was so impressed by the presents, that he exclaimed: "Good thing your parents gave you credit cards!"

Bob explained that those cards had already been confiscated by the parents of each, and that they had to spend cold hard cash. Albert continued: "We pooled our money, and I spent 50 cents more than 1/4 of the total amount. Bob spent a dollar more than half of what was left after I bought your present, and Cal spent $1.50 more than 3/4 of what was left then. At the end, we only had $5.50 left, so we were forced to share one Big Mac, medium fries and a medium drink."

How much did each spend on Don's present?
 
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  • #2
1234 (not the answer)
 
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  • #3
Forgive me, I can't find the button for math notations.
T = A + B + C

SA = T/4 + .5
SB = SA/2 + 1 = (T/4 + .5)/2 + 1
SC = (3/4)(SB) + 1.5 = (3/4)(SA/2 + 1) + 1.5 = (3/4)[(T/4 + .5)/2 + 1] + 1.5

T - SA - SB - SC = 5.5
T - (T/4 + .5) - [(T/4 + .5)/2 + 1] - [(3/4)[(T/4 + .5)/2 + 1] + 1.5] = 5.5
T - T/4 - .5 - T/8 - .25 - 1 - 3T/32 - .1875 - .75 - 1.5 = 5.5
17T = 310 (which is odd since it doesn't divide evenly)
 
  • #4
Albert $20
Bob $30
Cal $22.5

A+B+C=T-5.5
A=(T/4) + .5
B=(T-A)/2 +1
C=1.5+.75(T-A-B)
proceed from there
 
  • #5
ƒ(x) said:
Forgive me, I can't find the button for math notations.
T = A + B + C

SA = T/4 + .5
SB = SA/2 + 1 = (T/4 + .5)/2 + 1
SC = (3/4)(SB) + 1.5 = (3/4)(SA/2 + 1) + 1.5 = (3/4)[(T/4 + .5)/2 + 1] + 1.5

T - SA - SB - SC = 5.5
T - (T/4 + .5) - [(T/4 + .5)/2 + 1] - [(3/4)[(T/4 + .5)/2 + 1] + 1.5] = 5.5
T - T/4 - .5 - T/8 - .25 - 1 - 3T/32 - .1875 - .75 - 1.5 = 5.5
17T = 310 (which is odd since it doesn't divide evenly)

You don't need a "spoiler" unless you come up with an answer...
 
  • #6
$12.50

Here's why:

jpg0002.jpg
 
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  • #7
mugaliens said:
$12.50

Here's why:

jpg0002.jpg

That's not correct and your math is internally inconsistent. Even ignoring this, you've solved for the total, x, which is not the total spent, given the way you've set it up in the first line

You've set up x= spent + residual in the first line, but in the second line you indicate spent=x, based on the spent amounts you indicate for each in their respective boxes

Let's check my results:
Albert spent $20 according to my results. Is this $.50 more than one quarter of the total ?
Total = 20 + 30 + 22.5 + 5.5 = 78 > 1/4 of this is 19.50>>add .50 = 20 CHECK

I say Bob spent $30. Is this a dollar more than half of what was left after Albert spent ?
After Albert spent remainder = 78-20 = 58> 1/2= 29> +1=30 CHECK

I say Cal spent 22.5. Is this 1.5 more than 3/4 of what was left after Al and Bob spent ?
Remainder after Al and Bob=78-20-30=28 >> 3/4 = 21> +1.5= 22.5 CHECK

Finally, is their 5.50 left after all have spent ?

78-20-30-22.5=5.5 CHECK

But you knew you didn't have the correct answer, so the question is, why did you bother advertising that fact ?
 
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  • #8
regor60 said:
...why did you bother advertising that fact ?

I apologize - I'm new and wasn't aware of the spoiler tag policy.
 

Related to Solving Don's Birthday Gift Puzzle

1. How do you solve Don's Birthday Gift Puzzle?

To solve Don's Birthday Gift Puzzle, you will need to gather all the clues provided and carefully analyze them. Pay attention to details and think logically to figure out the correct answer.

2. What are the clues provided in Don's Birthday Gift Puzzle?

The clues provided in Don's Birthday Gift Puzzle are: the age of Don's mother, the number of candles on the cake, the cost of the gift, and the number of balloons.

3. How can I use the clues to solve Don's Birthday Gift Puzzle?

You can use the clues to solve Don's Birthday Gift Puzzle by creating a chart or list to organize the information. Then, use deductive reasoning to eliminate options and narrow down the possible solutions.

4. Is there a specific strategy to solve Don's Birthday Gift Puzzle?

There is no specific strategy to solve Don's Birthday Gift Puzzle, but it is recommended to carefully read and analyze each clue before making any assumptions. It may also be helpful to work backwards from the answer to ensure it meets all the given criteria.

5. Can the solution to Don's Birthday Gift Puzzle vary?

Yes, the solution to Don's Birthday Gift Puzzle can vary depending on the interpretation of the clues. It is important to carefully read and understand each clue to arrive at the correct solution.

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