A sweet sister cares for her little brother
One night, Alfred and Brenda won a sum of prize money after playing as a pair in a game show. Out of respect for his big sister who has taken good care of him over the years, Alfred split the money such that Brenda had the bulk.
However, Brenda was sad that her little brother, Alfred, did not have enough money. Being the generous girl that she is, she suggested giving Alfred $90 such that Alfred had thrice the amount of money as Brenda.
Touched by his big sister's sweetness, Alfred expressed that he was adamant about letting Brenda have the bulk. He suggested Brenda giving him just $20 such that she had twice the amount of money as him.
How much money did Brenda take at first?
The answer is 132.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Let Alfred's share be $a while Brenda's share be $b.
If Brenda were to give Alfred $90, we have a + 9 0 = 3 ( b − 9 0 ) which means a = 3 b − 3 6 0 .
If Brenda were to give Alfred just $20, we have 2 ( a + 2 0 ) = b − 2 0 which means 2 a = b − 6 0 .
Combining the two equations, we have:
2 ( 3 b − 3 6 0 ) = b − 6 0
6 b − 7 2 0 = b − 6 0
5 b = 6 6 0
b = 1 3 2