Adrianna has two brothers, Nate and Mark. Nate's age, n, is 11 less than the square of Mark's age, m, and Mark's age is 2 less than half of Nate's age.
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Adrianna has two brothers, Nate and Mark. Nate's age, n, is 11 less than the square of Mark's age, m, and Mark's age is 2 less than half of Nate's age.
Mark's age = 5 years
Nate's age = 14 years
Given,
Nate's age, n, is 11 less than the square of Mark's age, m
⇒ n = m^2 - 11
Mark's age is 2 less than half of Nate's age
⇒ m = n/2 - 2
Upon substituting the one in the other equation, we get,
m = (m^2 - 11)/2 - 2
⇒ 2m = m^2 - 11 -4
2m = m^2 - 15
m^2 - 2m - 15 = 0
(m-5)(m+3) = 0
m = -3, 5
As the age cannot be negative, therefore neglect negative value.
∴ m = 5
n = m^2 - 11
= (5)^2 - 11
= 25 - 11
∴ n = 14
Mark's age = 5 years
Nate's age = 14 years
Verification: Mark's age is 2 less than half of Nate's age
5 = 14/2 - 2
5 = 7 - 2
5 = 5
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