Question

Fatimah is 5 years older than Dollah. If the product of their ages is 234, how old is Dollah?

Answer 1

Data:

age of Dollah = x (unknown element)

age of Fatimeh = x + 5 (age of Dollah + 5)

the product is 234

Equation:

x * (x + 5) = 234

x² + 5x = 234

x² + 5x - 234 = 0

Δ = b² - 4 a c = 5² - 4 (1 * -234) = 25 - 4 (-234) = 25 - (-936)

= 25 + 936 = 961

x₁,₂=
`(b^(2) ± √(delta) )/(2a)` =
`(5^2 +/- √(961) )/(2)` =
`(25 +/- 31)/(2)`

x1 = (25+31)/2 = 56 / 2 = 28

x2 = (25 -31)/2 = -6 / 2 = -3 [age can't be negative, so the first one is accettable]

So:

Dollah's age (x) = 28 years old

Fatima's age (x + 5) = 28 + 5 = 32 years old