Bethany, Lauren, Amanda, and David all meet at a family reunion. They are comparing their ages. They have found that Lauren is 13 years older than Bethany and David is 11 years older than Amanda. They also found that the product of Bethany's and Lauren's ages is equal to twice Amanda's age. Also, if they subtract 20 years from both Bethany's and Lauren's age, the product is equal to David's age.If x represents Bethany's age and y represents Amanda's age, then which of the following systems of equations can be used to determine the ages of all four family members based on their findings?

Question

Answer:

Lauren =l
David=d
Bethany's =x
Amanda =y
l=x+13
d=y+11
lx=2y
(x+13)x=2y
[tex]2y=x^2+13x[/tex]
[tex]y= \frac{1}{2}(x^2+13x)[/tex]
or
[tex]y= \frac{x^2}{2}+ \frac{13}{2}x [/tex]
(x-20)(l-20)=d
(x-20)(x+13-20)=y+11
[tex]y+11=(x-20)(x-7)[/tex]
[tex]y+11=x^2-27x+140[/tex]
[tex]y=x^2-27x+129[/tex]
so I believe its b
Hope this helps :)

solved

general 11 months ago 1276