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?
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
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
Let's assume that Sheila initially had x dollars.
According to the given information, after Sheila gave $56 to Rita, Sheila would have x - 56 dollars, and Rita would have 5 times as much money as Sheila, which is 5 * (x - 56) dollars.
The total amount of money they had at first is $300, so we can form the equation:
x + 5 * (x - 56) = 300
Now let's solve this equation to find the value of x.
Expanding the equation:
x + 5x - 280 = 300
Combining like terms:
6x - 280 = 300
Adding 280 to both sides:
6x = 580
Dividing both sides by 6:
x = 96.67
Since money cannot be in cents, let's round down to the nearest whole number:
x ≈ 96
So Sheila had $96 initially.
To find how much Rita had, we can substitute this value of x into the expression we derived earlier:
5 * (x - 56) = 5 * (96 - 56) = 5 * 40 = $200
Therefore, Rita had $200 initially.