George and Vincent were given some income each. If George spent $28 each week and Vincent spent $56 each week, George would still have $837 left when Vincent spent all his income. If George spent $56 each week and Vincent spent $28 each week, George would still have $162 left when Vincent spent all his income

Question

George and Vincent were given some income each. If George spent $28 each week and Vincent spent $56 each week, George would still have $837 left when Vincent spent all his income. If George spent $56 each week and Vincent spent $28 each week, George would still have $162 left when Vincent spent all his income

(a) How much income did George receive?
(b) How much income did Vincent receive?

Answer 1

Set George receive x, Vincent receive y

(x - 837)/28 = y/56
y = 2(x - 837)
(x - 162)/56 = y/28
y = 1/2(x - 162)

2(x - 837) = 1/2 (x - 162)
4(x - 837) = x - 162
3x = 3186
x = 1026
y = 1/2 (1062 - 162) = 450
(a) George receive $1062
(b) Vincent receive $450