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Jon is 3 years younger than Laura. The product of their ages is 1,330. If [tex][tex]$j$[/tex][/tex] represents Jon's age and [tex][tex]$j+3$[/tex][/tex] represents Laura's age, what value of [tex][tex]$j$[/tex][/tex] could be Jon's age?

[tex]j=[/tex] ______________


Sagot :

Let's determine Jon's age given that Jon is 3 years younger than Laura and the product of their ages is 1,330.

1. Let [tex]\( j \)[/tex] represent Jon's age.
2. Therefore, Jon's age [tex]\( j \)[/tex] and Laura's age [tex]\( j + 3 \)[/tex] can be expressed using [tex]\( j \)[/tex].
3. Given that the product of their ages is 1,330, we can set up the following equation:
[tex]\[ j \times (j + 3) = 1330 \][/tex]
4. To find [tex]\( j \)[/tex], we solve the quadratic equation:
[tex]\[ j^2 + 3j - 1330 = 0 \][/tex]
5. Solving this equation, the potential solutions for [tex]\( j \)[/tex] are [tex]\( -38 \)[/tex] and [tex]\( 35 \)[/tex].

Since age cannot be negative, we discard [tex]\( -38 \)[/tex].

Thus, Jon's age, [tex]\( j \)[/tex], is:
[tex]\[ 35 \][/tex]

So, in the box, write:
[tex]\( \boxed{35} \)[/tex]
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