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Nell and David each have some money. If Nell gives David $16, both of

them will have the same amount of money. If David gives Nell $9, the

amount of money Nell has to the amount of money David has will be in

the ratio 6:1. How much money do the two boys have in all?

 Jan 12, 2022
 #1
avatar+13887 
+1

How much money do the two boys have in all?

 

Hello Ticon!

 

\(n-16\ $=d+16\ $\\ n=d+32\ $\\ (d-9\ $):(n+9\ $)=1:6\\ 6d-54\ $=n+9\ $\\ 6d-54\ $=d+32\ $+9\ $\\ 5d=95\ $\)

\(d=19\ $\\ n=51\ $\\ n+d=70\ $\)

laugh  !

 Jan 13, 2022
 #2
avatar+231 
+1

Let the amount of money Nell have = N,

And the amount of money David have = D

                              Nell         David

           Initiallly          N             D

           Case 1          N - 16      D + 16

           Case 2          N + 9       D - 9

Case 1 --> When Nell gives David $16,

         Then both have the same amount.

           So, N - 16 = D + 16

                     N = D + 16 + 16 = D + 32

Case 2 --> When David gives Nell $9,

            Nell and David's amount will be in

              The ratio 6:1.

                  (N + 9)/D - 9 = 6/1

                   N + 9 = 6D - 54

                   N = 6D - 63

After equating the equations from both cases,

We will get          N => D + 32 = 6D - 63

                                      32 + 63 = 6D - D

                                            95 = 5D

                                            D = 95/5 = $19

     And, N = D + 32
 Nell have $51 and David have

 $19. Together they have $(51 + 19)

                                        = $70

 Jan 14, 2022
edited by Slimesewer  Jan 14, 2022

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