Question

51,000 to start the

Julie and Kristen are partners in a local sporting goods shop. THey needed $51,
business. They invested in the ratio 5:12, respectively.

Answer 1

Part a) The amount of money invested by Julie was $15,000 and the amount of money invested by Kristen was $36,000

Part b) The percentage of business owned by Kristin was 70.6%

Part c) The percentage of business owned by Julie is 29.4%

Explanation:

The complete question is

Julie and Kristen are the partners in a local sporting goods shop. They needed $51,000 to start the business. They invested in the ratio 5:12,respectively.

a. How much money did each invest?

b. What percent of the business was owned by Kristin? Round to the nearest tenth of a percent.

c. If the business grows to $3,000,000, what percent of it will Julie own? Round to the nearest tenth of a percent.

Part a) How much money did each invest?

Let

x -----> amount of money invested by Julie

y ----> amount of money invested by Kristen

we know that

`x+y=51,000` -----> equation A

`(x)/(y) =(5)/(12)`

`x=(5)/(12)y` -----> equation B

substitute equation B in equation A and solve for y

`(5)/(12)y+y=51,000`

`(17)/(12)y=51,000`

`y=51,000(12)/17`

`y=\$36,000`

Find the value of x

`x=(5)/(12)(36,000)`

`x=\$15,000`

therefore

The amount of money invested by Julie was $15,000 and the amount of money invested by Kristen was $36,000

Part b) What percent of the business was owned by Kristin? Round to the nearest tenth of a percent.

we know that

They needed $51,000 to start the business

This amount represent the 100%

so

using proportion

Find out what percent of the business represent $36,000 (amount invested by Kristen)

Let

x ----> percentage of business owned by Kristin

`(100)/(51,000)=(x)/(36,000)\\\\x=36,000*100/51,000\\\\x=70.6\%`

therefore

The percentage of business owned by Kristin was 70.6%

Part c) If the business grows to $3,000,000, what percent of it will Julie own? Round to the nearest tenth of a percent.

we know that

The percentage of business owned by Kristin plus the percentage of business owned by Julie must be equal to 100%

Let

x ----> percentage of business owned by Kristin

y ----> percentage of business owned by Julie

`x+y=100\%`

we have

`x=70.6\%`

substitute and solve for y

`70.6\%+y=100\%`

`y=100\%-70.6\%`

`y=29.4\%`

therefore

The percentage of business owned by Julie is 29.4%