Question

Jack was 8 years older than Priscilla. Together their ages totaled 176 years. What were their ages?

Answer 1

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

`\begin{cases}x+8=y \\ x+y=176\end{cases}`

We can rewrite the first equation

`\begin{cases}x-y=-8 \\ x+y=176\end{cases}`

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

`\begin{gathered} x-y=-8 \\ x+y=176 \\ --------- \\ 2x+0y=168 \\ \to2x=168 \end{gathered}`

2. We can solve the sum for x

`\begin{gathered} 2x=168 \\ x=(168)/(2) \\ x=84 \end{gathered}`

3. We can replace x = 92 in one of the equations of the system and then solve it for y

`\begin{gathered} 84-y=-8 \\ 84+8=y \\ \to y=92 \end{gathered}`

Finally, we obtain that x = 84 and y = 92

ANSWER:

Jack was 92 years old.

Priscilla was 84 years old.