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.
[tex](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[/tex]
The number of years must be a positive number, so x=5.
The product of their ages will be 304 in 5 years.
