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. what percent of the business will joe own after he buys thea's portion

Answer 1

Joe originally owned 1/12 of the business. After buying Thea's share, he will own 5/12 of the business, which is approximately 41.67%.

Step-by-step explanation:

The question is asking how the ownership percentages of a partnership will change after one partner sells her share to another. Initially, Joe, Thea, and Taylor invested in a partnership in the ratio of 1:4:7, respectively. Years later, with the partnership worth 1.6 million, Thea decides to sell her portion to Joe.

To determine what percent of the business Joe will own after he buys Thea's portion, we must first calculate the individual shares based on the original investment ratio. The total parts of the investment are 1 (Joe) + 4 (Thea) + 7 (Taylor) = 12 parts.

Here's the breakdown:

• Joe's original portion is 1/12 of the business.
• Thea's portion is 4/12, or 1/3 of the business.
• Taylor's portion is 7/12 of the business.

After Thea sells her share to Joe, Joe's new share will be his original 1/12 plus Thea's 1/3, which can be calculated as follows:

Joe's new share = 1/12 + 4/12 = 5/12 of the business.

To convert this fraction to a percentage, we multiply by 100:

Joe's ownership percentage = (5/12) × 100 = approximately 41.67%.

So Joe will own about 41.67% of the business after purchasing Thea's portion.

Answer 2

Answer: 41.67%

Given:

If X=Joe’s investment in the business

4X= Thea’s investment

7X= Taylor’s investment

When it reached 1.6 million,

X+4X+7X=1,600,000

12x=1,600,000

X=1,600,000/12

X= 133,333.3 Joe’s investment

4x= 4(133,333.3)

=533,333.3 is Thea’s investment.

If this amount will be added to Joe’s, Joe’s investment will be 666,666.7 or 41.67% of the business