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Jon,Molly and Chris shared some sweets. The ratio of the total number of sweets received by Jon and Molly to the number of sweets received by Chris was 2:5 .when Chris gave 25 sweets to Jon And 31 sweets to Molly, and Jon gave gave 12 to Molly ,each had the same number of sweets. find the total number of sweets Jon had at first

Guest Mar 6, 2015

Best Answer 

 #1
avatar+91517 
+5

Mmm this is a long one.

J+25-12  =  M+12+31  =  C-31-25

J +13       =     M+43     =    C-56

J+M+13+43 = 2(C-56)

J+M+56 = 2C-112

J+M = 2C-168     (1)

 

J+M=(2/7)(J+M+C)         (2)

sub (1) into (2)                                 

2C-168=(2/7)(2C-168+C)  

2C-168=(2/7)(3C-168)                                                                           

7(2C-168)=2(3C-168)                                                                                  

14C-7*168=6C-2*168

8C = 5*168

C = 5*21

C = 105

 

M+43     =    C-56

M+43     =    105-56

M = 105-56-43

M =  6

 

J +13  =  M+43

J +13  =  6+43

J = 6+43-13

J= 36

 

Original number of lollies

 J= 36,  M =  6,    C = 105   

I have double checked that this fits with all the original information.

 

So originally Jon had 36 lollies 

Melody  Mar 6, 2015
Sort: 

1+0 Answers

 #1
avatar+91517 
+5
Best Answer

Mmm this is a long one.

J+25-12  =  M+12+31  =  C-31-25

J +13       =     M+43     =    C-56

J+M+13+43 = 2(C-56)

J+M+56 = 2C-112

J+M = 2C-168     (1)

 

J+M=(2/7)(J+M+C)         (2)

sub (1) into (2)                                 

2C-168=(2/7)(2C-168+C)  

2C-168=(2/7)(3C-168)                                                                           

7(2C-168)=2(3C-168)                                                                                  

14C-7*168=6C-2*168

8C = 5*168

C = 5*21

C = 105

 

M+43     =    C-56

M+43     =    105-56

M = 105-56-43

M =  6

 

J +13  =  M+43

J +13  =  6+43

J = 6+43-13

J= 36

 

Original number of lollies

 J= 36,  M =  6,    C = 105   

I have double checked that this fits with all the original information.

 

So originally Jon had 36 lollies 

Melody  Mar 6, 2015

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