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 By: verachen (offline)  Saturday, May 12 2012 @ 10:30 AM CDT (Read 1699 times)
verachen

Four boys, Alex, Bryan, Calvin and Derrick, each have some stamps.The number of stamps Alex has is 1/2 of the total of Bryan, Calvin and Derrick have. The number of stamps Bryan has is 1/3 of the total of Alex, Calvin and Derrick have. The number of stamps Calvin has is 1/4 of the total of Alex, Bryan and Derrick have. If Derrick has 78 stamps, find the total number of stamps Alex and Bryan have altogether.

Junior

Registered: 05/07/10
Posts: 15

 By: MathIzzzFun (offline)  Saturday, May 12 2012 @ 09:42 PM CDT
MathIzzzFun

Quote by: verachen

Four boys, Alex, Bryan, Calvin and Derrick, each have some stamps.The number of stamps Alex has is 1/2 of the total of Bryan, Calvin and Derrick have. The number of stamps Bryan has is 1/3 of the total of Alex, Calvin and Derrick have. The number of stamps Calvin has is 1/4 of the total of Alex, Bryan and Derrick have. If Derrick has 78 stamps, find the total number of stamps Alex and Bryan have altogether.

Hi

Total number of stamps remain unchanged.

A : B+C+D --> 1 : 2
A: A+B+C+D --> 1:3

B: A+C+D --> 1:3
B:A+B+C+D--> 1:4

C:A+B+D --> 1:4
C:A+B+C+D--> 1:5

A+B+C+D : A:B:C --> 60: 20: 15 : 12 : (60-20-15-12)
A+B+C+D : A:B:C --> 60units : 20units : 15units : 12units : 13units
13 units --> 78, 1 unit --> 6

A+B --> 35 x 6 = 210

cheers.

Chatty

Registered: 04/02/10
Posts: 36

 By: verachen (offline)  Saturday, May 12 2012 @ 11:00 PM CDT
verachen

Sorry but I don't really get why is it A : B : C : D --> 60 : 20 : 15 : 12?

Thanks.

Junior

Registered: 05/07/10
Posts: 15

 By: echeewh (offline)  Sunday, May 13 2012 @ 12:17 AM CDT
echeewh

Hey Vera,

Apply "Unchanged Total" concept (since all 3 comparisons are involving same A, B, C and D, and total number of stamps is the same in all 3 comparisons)

A : B+C+D | Total
1 : 2 3 --- (1)

B : A+C+D
1 : 3 4 --- (2)

C : A+B+D
1 : 4 5 --- (3)

Based on the concept, find lowest common multiple of 3, 4, 5. This gives 60. Hence, we have ...

(1)x 20:
20 : 40 60

(2)x 15:
15 : 45 60

(3)x 12:
12 : 48 60

Hence, A=20u, B=15u, C=12u, D=60u - 20u - 15u - 12u = 13u

Given D = 78 stamps, we have D = 13u --> 78
Therefore, 1u --> 78 / 13 = 6

A + B = 20u + 15u = 35u --> 35 x 6 = 210

===================================

Trust the above is now clear to you.

Cheers,
Edward

Active Member

Registered: 04/21/11
Posts: 627

 By: verachen (offline)  Sunday, May 13 2012 @ 09:06 AM CDT
verachen

Thank you for your help, both of you. I have understood how to do the question now. Thank you very much! ^.^

Junior

Registered: 05/07/10
Posts: 15

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