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

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