IDNStudy.com, kung saan ang iyong mga tanong ay natutugunan ng mga eksaktong sagot. Ang aming komunidad ay handang magbigay ng malalim at praktikal na mga solusyon sa lahat ng iyong mga katanungan.

Ana is 5 years older than Beth. In 5 years, the product of their ages is 1.5 times the product of their present ages. How old is Beth now?

Sagot :

Let x be Beth's age, since Ana is 5 years older, then
      x+5 would be Ana's age.

In five (5) years, Beth's age will be 5+x and Ana's age will be 5+(x+5). So,
Beth after 5 years = x+5
Ana after 5 years = x+10

The product of their ages 5 years after is 1.5 times the product of their present ages. Thus,
[tex](x+10)(x+5)=1.5x(x+5)[/tex]
[tex] x^{2} +15x+50=1.5 x^{2} +7.5x[/tex]
[tex] x^{2} -1.5 x^{2} +7.5x+50=0[/tex]
([tex]-0.5 x^{2} +7.5x+50=0[/tex] )(-2)        (Multiply both sides by -2)
[tex] x^{2} -15x-100=0[/tex]                    (Factoring)
[tex](x-20)(x+5)=0[/tex]
x=20; x=-5                           (x=-5 is rejected since we have no negative age)

So, the age of Beth now is 20; furthermore, Ana's age (x+5=20+5=25) is 25..