Let's solve this problem step-by-step:
1. Let [tex]\( j \)[/tex] represent Jon's age.
2. Since Jon is 3 years younger than Laura, Laura's age can be expressed as [tex]\( j + 3 \)[/tex].
3. The product of their ages is given as 1,330. Therefore, we can set up the equation:
[tex]\[
j \times (j + 3) = 1330
\][/tex]
4. Distribute [tex]\( j \)[/tex] through the parentheses to get a quadratic equation:
[tex]\[
j^2 + 3j = 1330
\][/tex]
5. Rearrange the equation to standard form:
[tex]\[
j^2 + 3j - 1330 = 0
\][/tex]
To find the values of [tex]\( j \)[/tex], you would normally solve this quadratic equation. The solutions to this equation are the possible values for Jon's age. The result of solving this quadratic equation yields:
[tex]\[
j = -38 \quad \text{or} \quad j = 35
\][/tex]
Since age cannot be negative, we discard -38. Therefore, Jon's age [tex]\( j \)[/tex] must be:
[tex]\[
j = 35
\][/tex]
Thus, the value of [tex]\( j \)[/tex] could be Jon's age is [tex]\( \boxed{35} \)[/tex].
