Asifpirlo wrote:

Mary and Mike enter into a partnership by investing $700 and $300 respectively. At the end of one year, they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business. If Mary received $800 more than Mike did, what was the profit made by their business in that year?

A. $2000

B. $6000

C. $4000

D. $1333

E. $3000

Since Mary and Mike invest $700 and $300, respectively, into the partnership, they will get 7/10 and 3/10 of the profit, respectively, after ⅓ of the profit is divided equally. In other words, Mary will get 7/10 and Mike will get 3/10 of the remaining ⅔ of the profit.

If we let x = the amount of profit in dollars, then Mary gets (½)(⅓)(x) + (7/10)(⅔)(x) = x/6 + 7x/15 dollars and Mike gets (½)(⅓)(x) + (3/10)(⅔)(x) = x/6 + x/5 dollars.

Since Mary gets $800 more than Mike, we have the following equation:

x/6 + 7x/15 = x/6 + x/5 + 800

7x/15 = x/5 + 800

Multiplying both sides by 15, we have:

7x = 3x + 12,000

4x = 12,000

x = 3,000

Answer: E

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