Question

Sheila and Rita had $300. After Shiela gave $56 to Rita, , Rita had 5 times as much money as Shiela . How much money did each of them have at first?

Answer 1

S = Sheila´s money

R = Rita´s money


Sheila and Rita had $300 mean:

S + R = 300


S + R = 300 Subtract S to both sides

S + R - S = 300 - S

R = 300 - S


After Shiela gave $56 to Rita, Shiela had:

S - 56 dollars

Rita had:

R + 56 = 300 - S + 56 = 356 - S


Rita had 5 times as much money as Shiela mean:

(356 - S ) / ( S - 56 ) = 5


Now:

( 356 - S ) / ( S - 56 ) = 5 Multiply both sides by ( S - 56 )

356 - S = 5 ( S - 56 )

356 - S = 5 S - 5 * 56

356 - S = 5 S - 280 Add S to both sides

356 - S + S = 5 S - 280 + S

356 = 6 S - 280 Add 280 to both sides

356 + 280 = 6 S - 280 + 280

636 = 6 S

6 S = 636 Divide both sides by 6

S = 636 / 6

S = $ 106


R = 300 - S = 300 - 106 = 194

R = $ 194


Proof:

After Shiela gave $56 to Rita, Shiela had S - 56 = 106 - 56 = $ 50

Rita had 194 + 56 = $ 250

250 / 50 = 5

Answer 2

Shiela's original amount --- x
Rita's amount = 300-x

after give-away:
Shiela had x-56
Rita had 300-x + 56 = 356-x

356-x - 5(x-56)
356-x = 5x - 280636 = 6x
x = 106

Shiela had $106 and Rita had $194