Solving Don's Birthday Gift Puzzle

[K Sengupta]

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?

 

[ƒ(x)]

1234 (not the answer)

 

[ƒ(x)]

Forgive me, I can't find the button for math notations.

Spoiler

T = A + B + C

S_A = T/4 + .5
S_B = S_A/2 + 1 = (T/4 + .5)/2 + 1
S_C = (3/4)(S_B) + 1.5 = (3/4)(S_A/2 + 1) + 1.5 = (3/4)[(T/4 + .5)/2 + 1] + 1.5

T - S_A - S_B - S_C = 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)

 

[regor60]

Spoiler

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

 

[regor60]

Forgive me, I can't find the button for math notations.

Spoiler

T = A + B + C

S_A = T/4 + .5
S_B = S_A/2 + 1 = (T/4 + .5)/2 + 1
S_C = (3/4)(S_B) + 1.5 = (3/4)(S_A/2 + 1) + 1.5 = (3/4)[(T/4 + .5)/2 + 1] + 1.5

T - S_A - S_B - S_C = 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...

 

[mugaliens]

Spoiler

$12.50

Here's why:

 

[regor60]

Spoiler

$12.50

Here's why:

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:

Spoiler

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 ?

 

[mugaliens]

...why did you bother advertising that fact ?

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