Allan gave 5/8 of his money to his son and then gave his daughter 1/2 of the remainder. He kept $150.00 for himself.
How much money did Allan have at the beginning?
How much money did his son get?
After giving to his son, he has 3x/8 left
after giving to his daughter he has 3x/16 left
3x/16 = 150
3x = 2400
x = 800
check:
first gift = (5/8)(800) = 500
amount left = 300
2nd gift = (1/2)(300) = 150
amount left = 150
Editorial:
Looks like sexism in continued in math questions.
Well, it would make it too easy if they both got the same amount. And sexism works both ways. You can't give the girl more money either.
To solve this problem, we can work backwards. We know that Allan kept $150.00 for himself, so we can subtract this amount from the final remaining amount to find out how much money he had before giving any to his son or daughter.
Let X be the amount of money Allan had at the beginning.
After giving 5/8 of his money to his son, Allan is left with 3/8*X.
After giving 1/2 of the remainder to his daughter, Allan is left with 1/2*(3/8*X) = 3/16*X.
We are given that Allan kept $150.00 for himself, so we can set up an equation:
3/16*X = $150.00
To solve for X, we can multiply both sides of the equation by the reciprocal of 3/16, which is 16/3:
(3/16*X)*(16/3) = ($150.00)*(16/3)
X = $150.00 * (16/3) = $800.00
Therefore, Allan had $800.00 at the beginning.
To find out how much money Allan's son got, we can multiply the amount Allan had at the beginning by 5/8:
$800.00 * (5/8) = $500.00
Therefore, Allan's son got $500.00.