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Alice and Bob each have a certain amount of money. If Alice receives n dollars from Bob, then she will have 4 times as much money as Bob. If, on the other hand, she gives n dollars to Bob, then she will have 8 times as much money as Bob. If neither gives the other any money, what is the ratio of the amount of money Alice has to the amount Bob has?

 Jul 31, 2023
 #1
avatar+757 
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Please stop spamming this question. The answer is no solution cuz u can't have a negative amount of money. You would be bankrupt. 

 Jul 31, 2023
 #3
avatar+832 
+1

 

As noted by my friend in Answer #1, this problem makes use of an unusual assumption.  However, it can be solved, although the value of "n" will require an amount of imagination.  Hey, the square root of minus one is an imaginary number, but that doesn't stop people from using it.  I'm solving the problem for you, so you can see how to solve it, whether or not the answer satisfies your sense of propriety. 

 

Alice and Bob each have a certain amount of money. If Alice receives n dollars from Bob, then she will have 4 times as much money as Bob. If, on the other hand, she gives n dollars to Bob, then she will have 8 times as much money as Bob. If neither gives the other any money, what is the ratio of the amount of money Alice has to the amount Bob has?    

 

                                        (A + n)  =  4 • (B – n)   

                                         A + n    =  4B – 4n    

                                         A – 4B  =  –5n                   (1)    

 

                                         (A – n)  =  8 • (B + n)   

                                          A – n    =  8B + 8n   

                                          A – 8B  =  9n                    (2)   

Multiply both sides  

of (1) by 9                        9A – 36B  =  –45n              (3)    

 

Multiply both sides  

of (2) by 5                        5A – 40B  =    45n              (4)      

 

Add (3) and (4)               14A – 76B  =  0   

 

Add 76B to both sides               14A  =  76B   

 

Divide both sides by 76B   

                                                  14A          1    

                                                  ––––   =   ––    

                                                  76B           1                       

 

Multiply both sides by 76/14    

                                                      A          76                         38

                                                    –––   =   –––   reduces to   –––   

                                                      B          14                          7   

 

It works if you accept the  

concept of negative money.  

That is, n must equal –2 dollars.    

 

Say Alice has 38 and Bob has 7        

                                                     (38 + n)  =  4 • (7 – n)     

                                                      38 + n   =  28 – 4n    

                                                             5n  =  –10     

                                                               n  =  –2       

and               

                                                     (38 – n)  =  8 • (7 + n)    

                                                      38 – n   =  56 + 8n      

                                                          –9n   =  18    

                                                               n  =  –2       

.

 Aug 1, 2023

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