Question

Audra's parents are both in their forties. The sum of their ages is ninety-two. The product of their ages is 2,107. How old is Audra's oldest parent?A.43B.45C.47D.49

Answer 1

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

`\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}`

Represent the first statement with an equation: The sum of their ages is ninety-two

`x+y=92`

Represent the second statement with an equation: The product of their ages is 2,107.

`xy=2107`

Combine the two equations to determine the value of x and y using substitution method

Make x the subject of equation 1

`\begin{gathered} x+y=92 \\ x=92-y \end{gathered}`

Substitute x into equation 2

`\begin{gathered} xy=2107 \\ (92-y)y=2107 \\ 92y-y^2=2107 \\ -y^2+92y-2107=0 \end{gathered}`
`\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}`

Substitute for y in equation 1

`\begin{gathered} x=92-y,y=43 \\ x=92-43,x=49 \\ y=49 \\ x=92-49 \\ x=43 \end{gathered}`

Hence, Audra's older parent age is 49, OPTION D