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

Answer:

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%

Step-by-step 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

$\frac{x}{y} =\frac{5}{12}$

$x=\frac{5}{12}y$ -----> equation B

substitute equation B in equation A and solve for y

$\frac{5}{12}y+y=51,000$

$\frac{17}{12}y=51,000$

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

$y=\ 36,000$

Find the value of x

$x=\frac{5}{12}(36,000)$

$x=\ 15,000$

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

$\frac{100}{51,000}=\frac{x}{36,000}\\\\x=36,000*100/51,000\\\\x=70.6\%$

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%