Question

Shirley owns 7 1/2 shares of a stock. The stock's closing value one day was 10 1/5 per share. During that day, the value of the stock had changed such that the total change on all her shares was −8 1/4 . What was the opening value on each share of that stock that day? Enter your answer as a mixed number in simplest form in the box.

Answer 1

To find the opening value of each share, we set up an equation using the given information. By solving the equation, we determine that the opening value was $15.70.

Step-by-step explanation:

To find the opening value of each share on that day, we need to use the given information and solve an equation.

We know that Shirley owns 7 1/2 shares of the stock and the total change on all her shares is -8 1/4.

Let's assume the opening value of each share was x.

So, the closing value of each share would be x - (8 1/4 ÷ 7 1/2).

We can calculate the value:

1. Convert 7 1/2 to an improper fraction: 7 1/2 = 15/2.
2. Convert 8 1/4 to an improper fraction: 8 1/4 = 33/4.
3. Divide 33/4 by 15/2: 33/4 ÷ 15/2 = 33/4 x 2/15 = 11/2.
4. Subtract 11/2 from x: x - 11/2.

Now, we know the closing value of each share is 10 1/5.

1. Convert 10 1/5 to an improper fraction: 10 1/5 = 51/5.
2. Set up the equation: x-11/2 = 51/5.
3. Multiply both sides of the equation by 10 to get rid of the fraction: 10(x - 11/2) = 10(51/5).
4. Simplify: 10x - 55 = 102.
5. Add 55 to both sides of the equation: 10x - 55 + 55 = 102 + 55.
6. Simplify: 10x = 157.
7. Divide both sides of the equation by 10: x = 15.7.

Therefore, the opening value on each share of that stock that day was $15.70.