Answer :
Given: Word problem leading to simultaneous equation involving the ages of Audra's parents
To Determine: The age of Audra's older parent
Represent the ages with unknown
[tex]\begin{gathered} L_{et\text{ the age of Audra's older parent}}=x \\ L_{et\text{ the age of Audra's younger parent }}=y_{} \end{gathered}[/tex]Represent the first statement with an equation: The sum of their ages is ninety-two
[tex]x+y=92[/tex]Represent the second statement with an equation: The product of their ages is 2,107.
[tex]xy=2107[/tex]Combine the two equations to determine the value of x and y using substitution method
Make x the subject of equation 1
[tex]\begin{gathered} x+y=92 \\ x=92-y \end{gathered}[/tex]Substitute x into equation 2
[tex]\begin{gathered} xy=2107 \\ (92-y)y=2107 \\ 92y-y^2=2107 \\ -y^2+92y-2107=0 \end{gathered}[/tex][tex]\begin{gathered} -y^2+43y+49y-2107=0 \\ y^2-92y+2017=0 \\ y^2-43y-49y+2017=0 \\ y(y-43)-49(y-43)=0 \\ (y-43)(y-49)=0 \\ y-43=0,or,y-49=0 \\ y=43,or,y=49 \end{gathered}[/tex]Substitute for y in equation 1
[tex]\begin{gathered} x=92-y,y=43 \\ x=92-43,x=49 \\ y=49 \\ x=92-49 \\ x=43 \end{gathered}[/tex]Hence, Audra's older parent age is 49, OPTION D
