What was the total amount of the lottery winnings?

Question

When her mother won a lottery ticket, Kayla was given 1/3 of the prize money.  Each of her four brothers received 1/4 of the remaining money.  When Kayla and one of her brothers put their money together, they had $75,000.  What was the total amount of the lottery winnings?

Answer 1

Hi, Catrina -

 

To solve this word problem, it is best to start by assuming a value (let's say "x") for the unknown value being requested which is the total amount of lottery winnings.

 

So based on the word problem, we know Kayla received (1/3)x which is 1/3 of the lottery winnings.

 

We know that each of the 4 brothers received 1/4 of the remainder of the winnings.  The remainder of the winnings would be x - (1/3)x. So each brother would receive 1/4 of this value or 

(1/4)[x - (1/3)x].

 

Because it says that Kayla and one of her brothers put their money away and it was $75,000, you can set up the equation:

(1/3)x + (1/4)[x- (1/3)x] = 75,000

 

You can then solve this equation for x. Because x is the amount we assumed for the total lottery winnings that will answer the problem.