Question

If twice the age of a stamp is added to the age of a coin, the result is 45. The difference between three times the age of a stamp and the age of a coin is 5. What is the age of the stamp?

Answer 1

10 years

1) Considering that we can call the age of a stamp by "s" and the age of a coin by "c" we can write out the following system of Linear Equations:

`\begin{gathered} 2s+c=45 \\ 3s-c=5 \end{gathered}`

Note that we can solve it using the Elimination Method.

2) So let's add simultaneously both equations:

`\begin{gathered} 2s+c=45 \\ 3s-c=5 \\ -------- \\ 5s=50 \\ (5s)/(5)=(50)/(5) \\ s=10 \end{gathered}`

We can plug into that s=10 and find the age of a coin as well:

`\begin{gathered} 2(10)+c=45 \\ c=45-20 \\ c=20 \end{gathered}`

Note that we subtracted 20 from both sides.

3) Hence, the age of a stamp is 10 years