algebra with finance word problem

Question

Joe, Thea, and Taylor invested in a partnership in the ratio 1:4:7, respectively. Years later, when the partnership was worth $1.6 million, Thea decides to go to graduate school and sells her part of the partnership to Joe.

 

a) how much would Joe need to pay Thea to buy her share of the business?

b) what percent of the business will Joe own after he buys Thea's portion?

Answer 1

Hi, Tiffanie.

 

You'll want to set this up using an equation.  Let x represent the smallest part, which would be Joe's.

 

x = Joe

 

4x = Thea

 

7x = Taylor

 

Your equation is now 1x + 4x + 7x = 1,600,000.

 

Combine like terms to get 12x = 1,600,000

 

Solving for x gets you $133,333.33.  (Each person will end up having $0.33, but we'll worry about that later.)  Plug that in to what you originally had.

 

$133,333.33 (rounded)= Joe

 

4(133,333.33) = $533,333.33 (rounded)= Thea

 

7(133,333.33) = $933,333.33 (rounded)= Taylor

 

So, if Joe wants to buy out Thea, he has to pay her about $533,333.  Then, if you add together his share and her share, you get $133,333 + $533,333, which gives you $666,666.  (Ignoring the cents.)  Divide that by the total of $1,600,000 gives you about 41% of the business.

Answer 2

Many problem statements have extra information that is intended to make it sound realistic and to keep our interest in “real-world” applications of math.  The finance portion of this problem may be ignored.  

The problem can be restated as: 
                            The proportion  of A:B:C is 1:4:7 and totals 1.6M
                            (a) what is the value of B?
                            (b) what is the combined value of A+B (as a %)?

Rewrite the proportion by dividing each term by the total (which is 12).
           The proportion of A:B:C: is  1/12 : 4/12 : 7/12  and totals 1.6M
           So, what is B?     B = (4/12)*(1.6M)        [4/12 of 1.6M]
                                         B = 0.533M

           And, what is combined value of A+B?
                                     A+B = (1/12)*1.6M + (4/12)*1.6M
                                      A+B = (5/12)*1.6M
                                      A+B = 0.667M

(note:  if they have been business together for “years,” they will know precisely when to round off the dollar amount)

The new ratio is   5 : 7.     This means that Thea now owns 5/12, or 41.7% (rounded).

Answer 3

The assets are in 12 "shares," 1 + 4 + 7

Thea owns 4/12 or 1/3 of the assets

(1/3)1.6 million = 0.5333 million

Joe needs to pay Thea $533,333.33

Joe shall now own 5/7 or 0.714285714 or 71.43% (rounded)