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Luis and Jack had 350 marbles altogether. Luis gave away 25% as many marbles as Jack. Jack was left with 40 more than the number of marbles he gave away? Luis had 25% as many marbles as Jack in the end. How many marbles did Jack have in the end?

 Apr 19, 2021
 #1
avatar+121004 
+2

Let  the  number  that  Jack  gave  away  = G

Then Luis  gave away  .25G

 

Number  that  Jack  had  remaining =    G +  40

So Jack  must  have  started  with  G + G + 40   =    2G  +  40

 

And Luis   must  have started  with  (.25)G  + .25(G + 40)   =  .5G  + 10

 

So

 

(2G + 40)  +  (.5G  + 10) =  350

 

2.5G  +  50  =   350

 

2.5G  = 350  -  50

 

2.5G  =  300

 

G = 300  / 2.5 

 

G = 120

 

Jack  had   120  +  40  =  160  at  the  end

 

Proof

 

Jack   started  with    2(120) + 40  =  280 

Luis  started  with .5(120)  +  10   =   70

 

Jack  gave  away  120   and ended  up with  160  = 40  more  than he gave  away

 

Luis gave  away  (.25)(120) =  30

And  he ended up with  40   =  .25 of (160)

 

 

cool cool cool

 Apr 19, 2021
 #2
avatar+290 
+2

Good job CPhill 👏👏👏

Tgfromthe4  Apr 19, 2021
 #3
avatar+121004 
+1

THX   !!!

 

 

cool cool cool

CPhill  Apr 19, 2021

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