Question

The ages of two sisters are 11 years and 14 years.In how many years time will the product of their age be 304?

Answer 1

x - the number of years in which the product of their ages will be 304
In x years one sister will be 11+x years old, and the other sister will be 14+x years old.


`(11+x)(14+x)=304 \\ 154+11x+14x+x^2=304 \\ x^2+25x+154=304 \\ x^2+25x-150=0 \\ x^2-5x+30x-150=0 \\ x(x-5)+30(x-5)=0 \\ (x+30)(x-5)=0 \\ x+30=0 \ \lor \ x-5=0 \\ x=-30 \ \lor \ x=5`

The number of years must be a positive number, so x=5.

The product of their ages will be 304 in 5 years.