Question

Jamal is 8 years older than Autumn. In 2 years the sum of their ages will be 70. How old is Jamal now?

Answer 1

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

`J=A+8`

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

`(A+2)+(J+2)=70`

We reduce like terms

`A+J+4=70`

Then, we subtract 4 on each side

`\begin{gathered} A+J+4-4=70-4 \\ A+J=66 \end{gathered}`

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

`\begin{gathered} A+A+8=66 \\ 2A+8=66 \end{gathered}`

We subtract 8 on each side

`\begin{gathered} 2A+8-8=66-8 \\ 2A=58 \end{gathered}`

At last, we divide the equation by 2

`\begin{gathered} (2A)/(2)=(58)/(2) \\ A=29 \end{gathered}`

Therefore, Autumn is 29 years old.

Let's find Jamal's age.

`J=29+8=37`

Therefore, Jamal is 37 years old.