Rs 366 are divided amongst A B and C so that A may get 1/2 as

Question

Rs 366 are divided amongst A B and C so that A may get 1/2 as much as B & C together. B may get 2/3 as much as A&C together then share of is A

 

how to solve this problem by using one variable 

and how to solve this problem by using two varible?

Answer 1

1) setup formulas

A + B + C = 366
A = (B+C)/2
B = (A+C) * 2/3

2) isolate variables to get them all in terms of c

366 - b- c = (b+c)/2
732 - 2b -2c = b+c
732 - 3c = 3b
244 - c =b

244 - c = (a + c)(2/3)
366 - 3c/2 = a +c
366 - 5c/2 = a

3) plug back into equation 1 and solve for c

(366 - 5c/2) + (244 - c) + c = 366
244 - 5c/2 = 0
244 = 5c/2
488 = 5c
97.6 = c

4) now use c to solve for a and b

244 - 97.6 = b
146.4 = b

366 - 5(97.6)/2 = a
122 = a

5) check your answers in the original equations

122 + 146.4 + 97.6 = 366
366 = 366

122 = (146.4+97.6)/2
122 = 122

146.4 = (122+97.6) * 2/3
146.4 = 146.4