Samantha, Nyla, and Jerry own shares of stock in the Triumph Hotels company. The shares of stock that they own have a combined value of $6,880. Samantha owns 70 shares, Nyla owns 50 shares, and Jerry owns 40 shares. What is the value of the shares Samantha owns?

Options

A. $ 98
B. $ 301
C. $3,010
D. $4,816

Answer

To find the value of the shares that Samantha owns, we can follow these steps:

### Step 1: Calculate the total number of shares owned by Samantha, Nyla, and Jerry.
- Samantha owns 70 shares.
- Nyla owns 50 shares.
- Jerry owns 40 shares.

**Total shares = 70 + 50 + 40 = 160 shares.**

### Step 2: Determine the total value of all shares.
- The combined value of all shares is given as $6,880.

### Step 3: Find the fraction of shares owned by Samantha.
- The fraction of shares owned by Samantha is calculated as:

**Fraction of shares owned by Samantha = (Number of shares owned by Samantha) / (Total number of shares)**

**Fraction = 70 / 160.**

### Step 4: Calculate the value of Samantha's shares.
- To find the value of Samantha's shares (let's denote it as V), we can use the formula:

**V = (Fraction of shares owned by Samantha) × (Total value of shares)**

Substituting the values we have:

**V = (70 / 160) × 6880.**

### Step 5: Simplify the calculation.
- First, simplify the fraction:

**70 / 160 = 7 / 16.**

- Now substitute this back into the equation for V:

**V = (7 / 16) × 6880.**

### Step 6: Perform the multiplication.
- Calculate the value:

**V = 7 × (6880 / 16).**

- First, divide 6880 by 16:

**6880 ÷ 16 = 430.**

- Now multiply by 7:

**V = 7 × 430 = 3010.**

### Conclusion:
- The value of the shares that Samantha owns is **$3,010.**

---