Question

Amira is twice as old as her cousin Pam. Nine years ago, their combined age was 18. What are their present ages?

Answer 1

Amira is currently 24 years old and Pam is currently 12 years old

Explanation:

Let Amira's age be
`a` and Pam's age be
`p`. Currently, Amira is twice as old as Pam. Therefore, we can write the equation
`a=2p`.

We can write a second equation using the other information given in the question. Nine years ago, Amira and Pam's combined ages was 18. If Amira and Pam are currently
`a` and
`p` years old, respectively, then their respective ages 9 years ago would ben
`a-9` and
`p-9`. Since these add up to 18, we have the equation
`(a-9)+(p-9)=18`.

Therefore, we have a system of equations:

`\begin{cases}a=2p,\\a-9+p-9=18\end{cases}`

Substitute the first equation into the second one:

`2p-9+p-9=18`

Combine like terms:

`3p-18=18`

Add 18 to both sides:

`3p=36`

Divide both sides by 3:

`p=(36)/(3)=\boxed{12}`

Now substitute this into any of the equations (I'll choose the first):

`a=2p,\\a=2(12),\\a=\boxed{24}`

Therefore, Amira is currently 24 years old and Pam is currently 12 years old.