Sam and Jeremy have ages tha are consecutive odd integers. The product of their ages is 783. Which equation could be used to find Jeremy's age, j, if the he is the younger man?

Options

A. `j^(2)+2=783`
B. `j^(2)-2=783`
C. `j^(2)+2j=783`
D. `j^(2)-2j=783`

Answer

To find Jeremy's age, we can follow these steps:

1. **Define the Variables**:
Let Jeremy's age be represented as \( j \). Since Sam is older and their ages are consecutive odd integers, Sam's age can be expressed as \( j + 2 \).

2. **Set Up the Equation**:
According to the problem, the product of their ages is 783. Therefore, we can set up the equation:
\[ j \times (j + 2) = 783 \]

3. **Expand the Equation**:
Expanding the left side gives us:
\[ j^2 + 2j = 783 \]

4. **Rearrange the Equation**:
To form a standard quadratic equation, we can rearrange it as:
\[ j^2 + 2j - 783 = 0 \]

5. **Identify the Equation**:
The equation we derived, \( j^2 + 2j - 783 = 0 \), can be used to find Jeremy's age.

**Final Equation**:
Thus, the equation that could be used to find Jeremy's age \( j \) is:
\[ j^2 + 2j - 783 = 0 \]