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

Answer:

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

Step-by-step 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:

$p=\frac{36}{3}=\boxed{12}$

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.