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Leo and Isaac had 95 marbles altogether. Leo gave away 3 more marbles than Isaac. Isaac was left with 5 fewer than the marbles he gave away. Leo had 2 more marbles left than Isaac. How many marbles did Leo give away?

 

Draw a model by using the information in the question.

 Apr 21, 2021
 #1
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Let  Leo  start with  N  marbles

Then Issac  started with  95 - N  marbles

 

Let  the  number of  marbles that Issac gave away  = G

Then Leo  gave away  G +  3

 

From Issac's  point of view

 

(95 - N)  - G   =  G  - 5

95 - N  = 2G- 5

95 + 5 - 2G  = N

100  - 2G  = N      (1)    

 

From Leo's point of  view

 

N  -  (G + 3)   =  (G - 5)  + 2

N - G - 3  =  G -  3

N =  2G       (2)

 

Equating  (1)  and (2)   we  have

 

100 - 2G =  2G

 

100 =  4G

 

100 / 4 = G   =   25

 

So Leo  gane away  G + 3   =   28  marbles

 

Proof

N = 2G  = 50 = what Leo started with

95 - 50  =  45  = what Isaac started with

 

Leo gave  away  28   and  was  left  with 22

Isaac  gave away 25  and  was left  with  20

And Leo was left with two more marbles  than Isaac

 

cool cool cool

 Apr 21, 2021

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