Question

Linear equation topic. (Lisa is 5 years younger than his elder brother,Daniel.The product of their ages is 2/3 of their grandmother's age.If their grandmother is 54 years old,find Daniel's age.)

Answer 1

Let Daniel's age be 'x' years , hence, Lisa's age is (x - 5) years. Let Grandma's age be 'y' = 54 years.
Hence,
x(x - 5) = 2/3 × y
x² - 5x = 2 × 54 years / 3
x² - 5x = 36 years
x² - 5x - 36 = 0
∆ = (-5)² - 4(1)(-36) = 25 + 144 = 169
√∆ = √169 = 13
$x\: = \: \frac{ - b \: \frac{ + }{ } \: \sqrt{ {b}^{2} \: - \: 4ac} }{2a}$
x1 = (5+13)/2, x2 = (5-13)/2
x1 = 9, x2 = -4
Since, age can't be negative,
Daniel's age = x = 9 years.