Alex and Rachel agreed to form a partnership. The partnership agreement requires that Alex

invest $3000 more than two - third of what Rachel is to invest. If the partnerships' capital is to be

$55,000, how much should Alex invest?

Alex investment = $ 23,800

Step-by-step explanation:

The statement is Alex and Rachel are forming partnership. According to the agreement Alex invest $3000 more than Rachel's two-third investment and the total capital is $55,000. Find out Alex investment.

Let x be the investment of Rachel. Lets make an equation to find the value of x.

x+2/3x + $3000=$55,000

Combine the like terms:

x+2/3x = 55,000 - 3000

x+2/3x = $52000

Now take the L. C. M of L. H. S

3x+2x/3 = $52000

Now Add the values of x.

5x/3 = $52000

Multiply both the terms by 3.

5x/3 * 3 = 3 * $52000

5x = 156000

Now divide both the sides by 5.

5x/5 = 156000/5

x = 31200

Now calculate Alex investment. According to the statement Alex invest $3000 more than 2/3 of Rachel.

We have found the Rachel investment which is $31200. Therefore we can write 2/3 of Rachel investment as 2/3 (31200).

=2/3 (31200) + $3000

=2*10400+3000

=20,800+3000

=$23,800

Rachel investment = $31200

Alex investment = $ 23,800

If you want to check whether the investments are correctly determined or not. You can add both the investments and the result will be the partnership's capital amount.

$31200+$ 23,800 = $55,000 ...