Adam, Bill, Chris, and Dave each own one quarter of a company. Bill sells
2/3 of his shares to Dave. Adam sells 3/5 of his shares to Chris and the
rest to Dave. How much of the company does Dave own now? Give your
answer as a fraction reduced to simplest terms.
Assistance needed.
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Originally Dave has 1/4. He receives 2/3 *1/4 shares from Bill and 2/5 * 1/4 shares from Adam. Multiply first and then add and reduce.
I hope this helps.
To solve this problem, we need to calculate the shares each person initially owns and then determine how much of the company Dave owns after the transactions.
Let's start by determining the initial shares owned by each person:
If Adam, Bill, Chris, and Dave each own one quarter of the company, it means they each own 1/4 of the company.
Now let's calculate the shares after the transactions:
Bill sells 2/3 of his shares to Dave. Since Bill initially owned 1/4 of the company, he now has (1/4 * (1 - 2/3)) = 1/4 * 1/3 = 1/12 of the company.
Adam sells 3/5 of his shares to Chris and the rest to Dave. If Adam initially owned 1/4 of the company, he sells (1/4 * 3/5) = 3/20 of the company to Chris.
The remaining shares that Adam sold to Dave = (1/4 - 3/20) = 5/20 - 3/20 = 2/20 = 1/10 of the company.
Adding up the shares bought by Dave:
Dave bought 1/12 of the company from Bill and 1/10 of the company from Adam. So, Dave now owns (1/12 + 1/10) = (5/60 + 6/60) = 11/60 of the company.
Therefore, after the transactions, Dave owns 11/60 of the company.