Answer :
We know that
- Jack was 8 years older than Priscilla
- Together their ages totaled 176 years
And we must find their ages
To find their ages we can use a system of equations that represents the situation
[tex]\begin{cases}x+8=y \\ x+y=176\end{cases}[/tex]We can rewrite the first equation
[tex]\begin{cases}x-y=-8 \\ x+y=176\end{cases}[/tex]Where,
x represents the age of Priscilla
y represents the age of Jack
Now, we must solve the system
1. We can add up the two equations
[tex]\begin{gathered} x-y=-8 \\ x+y=176 \\ --------- \\ 2x+0y=168 \\ \to2x=168 \end{gathered}[/tex]2. We can solve the sum for x
[tex]\begin{gathered} 2x=168 \\ x=\frac{168}{2} \\ x=84 \end{gathered}[/tex]3. We can replace x = 92 in one of the equations of the system and then solve it for y
[tex]\begin{gathered} 84-y=-8 \\ 84+8=y \\ \to y=92 \end{gathered}[/tex]Finally, we obtain that x = 84 and y = 92
ANSWER:
Jack was 92 years old.
Priscilla was 84 years old.