Maths problem. Please help

Natalie is 3 years younger than one brother and 8 years younger than her eldest brother. The product of their brothers ages is equal to the age of her mother who is 50. How old is Natalie?

Please show full working out. Thank you

Let Natalie age = x
then age of first brother = (x + 3)
and age of eldest brother = (x + 8)
(x + 3)(x + 8) = 50
x² + 11x + 24 = 50
x² + 11x – 26 = 0
(x + 13)(x – 2) = 0
x = 2 ---------------- taking + ve value of x


Natalie age = 2 years
then age of first brother = 5 years
and age of eldest brother = 10 years
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Natalie's Age = N
Older Brother = B
Other Brothe = A

Three Unknowns, Three Equations
1.) A = N + 3
2.) B = N + 8
3.) AXB = 50

Natalie is 3 years younger than brother A. (Eq. 1.)
Natalie is 8 years younger than brother B. (Eq. 2)
The product (multiplication) of A and B is 50.

Plugging Eq. 1 and Eq. 2 into Eq. 3:

(N+3)(N+8) = 50
N^2 + 11N + 24 = 50
N^2 + 11N - 26 = 0

Using the Quadratic Equation:
N = 0.5 * (-11 + sqrt(11^2 - (4*-26)))
N = 2 (the only positive answer)

Natalie is 2 years old.
Brother A is 5 years old.
Brother B is 10 years old.

If this helped, remember to give me best answer! Thank you.

Let Natalie's age be x years

One brother = x+3 years

Eldest = ( x+8) years

( x+8) ( x+3) = 50

x^2 + 11x +24 = 50

x^2 + 11x -26 = 0

( x+13) ( x-2) = 0

x =2

ANSWER Natalie = 2 years
Brothers are 5, & 10 years

Natalie is x years old.
Her brothers are (x+3) and (x+8).
(x+3)(x+8) = 50
x+3=5 and x+8=10, so x=2

Natalie is 2 years old.