Andy and Bruce had some money. Andy had 50% more money than Bruce. After Andy gave Bruce $77, Bruce had 25% more money than Andy.
(a) How much money did they have in total?
(b) How much money must Bruce then give to Andy so that Andy wouldl have 50% more money than Bruce?
(a) According to the information,
x = 1.5y (1)
y + 77 = 1.25 (x - 77) (2)
x = 297, y = 198
x + y = 297 + 198 = $495
They have $495 in total.
(b) Let the money that Bruce then give to Andy be a.
After Andy gave Bruce $77, Andy had 297 - 77 = $220
Bruce had 198 + 77 = $275
220 + a = 1.5 (275 - a)
a = 77
Bruce must give Andy $77 so that Andy would have 50%
more money than Bruce
B = what Bruce had to start with
1.5 B = what Andy had to start with
And we know that
(1.5B - 77) *1.25 = B + 77 simplify
1.875B - 96.25 = B + 77
1.875B - B = 77 + 96.25
.875B = 173.25
B = 173.25 / . 875 = $198 = what Bruce started wih
1.5 B = $297 = what Andy started with
a) They had 198 + 297 = $495 in total
b) If Bruce returns the $77 to Andy....the original relationship still holds....Andy has 50% more money than Bruce