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# mathematics

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Caleb had 37 more marbles than David at first. Caleb gave away 4 times as many marbles as David. David was left with 5 more than the number of marbles he gave away. Caleb had twice as many marbles left as David. How many marbles did Caleb have in the end?

Apr 19, 2021

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Let  the number   that   David  had at first =  D

Then Caleb  had  D + 37

Caleb  gave away  4G

David  gave  away  G

And  we  have  this sysyem

D - G  =  G  + 5      ⇒     D = 2G +5       (1)

(D + 37)  - 4G  =  2 (D - G)                   (2)

Sub ( 1)  into  (2)  for D

(2G+ 5 + 37)  - 4G  =  2 ( 2G + 5 - G)

-2G  +  42   =  2( G + 5)

-2G  + 42 =  2G + 10

42  - 10 =  2G + 2G

32  =  4G

32/4  =  G = 8

D=  2(8)  +  5   =  21

C  =  21  + 37  =  58

Proof

Caleb started  with  58  and gave away 4(8) =  32    he ended  up  with  26

David  started  with 21   gave away 8  and  ended up  with  13

And Caleb  had  twice  as many left as David

Apr 19, 2021
edited by CPhill  Apr 19, 2021