Respuesta :

We know that

• Jamal is 8 years older than Autumn.

,

• In 2 years the sum of their ages will be 70.

Each statement above has to be expressed as an equation. Notice that "8 years older" means +8. So, the equation about the first statement is

[tex]J=A+8[/tex]

Now, "in 2 years" means we have to add 2 units to each age, also we have to add them to get 70. The equation about the second equation is

[tex](A+2)+(J+2)=70[/tex]

We reduce like terms

[tex]A+J+4=70[/tex]

Then, we subtract 4 on each side

[tex]\begin{gathered} A+J+4-4=70-4 \\ A+J=66 \end{gathered}[/tex]

Now, we replace the first equation into the last one above.

[tex]\begin{gathered} A+A+8=66 \\ 2A+8=66 \end{gathered}[/tex]

We subtract 8 on each side

[tex]\begin{gathered} 2A+8-8=66-8 \\ 2A=58 \end{gathered}[/tex]

At last, we divide the equation by 2

[tex]\begin{gathered} \frac{2A}{2}=\frac{58}{2} \\ A=29 \end{gathered}[/tex]

Therefore, Autumn is 29 years old.

Let's find Jamal's age.

[tex]J=29+8=37[/tex]

Therefore, Jamal is 37 years old.