Nikki is 5 years older than Jamie. The product of their ages is 126. Which equation could be used to find Nikki’s age, n?

The equation find Nikki's age is n² - 5n = 126

From the given statement we can deduce the following and form equation to find Nikki's age.

Let the age of Nikki = n

Let the age of Jamie = y

From the first statement:

                                                                 n - 5 = y

From the second statement:

                                                      n(n - 5) = 126

Simplify the equation as follows;

n(n - 5) = 126

n² - 5n = 126

Thus, the equation find Nikki's age is n² - 5n = 126

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Let, Nikki's age is 'n'.

Since, Jamie is 5 years younger than Nikki, let Jamie's age be 'n-5'

According to the question,

The product of their age is 126.

which means,

Nikki's Age × Jamie's age = 126

⇒ n × (n-5) = 126

⇒ n² - 5n = 126

⇒ n² - 5n - 126 = 0

Now you can do the middleterm,

⇒n² - 14n + 9n - 126 =0

⇒ n ( n - 14 ) + 9 (n - 14 ) = 0

⇒ ( n - 14 ) ( n + 9 ) = 0

since n's value can not negative

⇒ ( n - 14 ) = 0

∴ n = 14

Nikki's age is 14

and Jamie's age is 9 years

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