Question

Use the expressions from the previous questions to determine Mary’s age.

Answer 1

The age of Mary is 15 years old.

To solve this, we have three expressions:

`\begin{gathered} M=J+5 \\ J=T-28 \\ T=3H-1 \end{gathered}`

Where M is the age of Mary, J is the age of Jacob, T is the age of Uncle Tim and H is the age of Henry

Also teh problem give us an additional info, the age of Henry is 13. With this, we can replace the value of H in the thrid equation:

`\begin{gathered} \begin{cases}H=13 \\ T=3H-1\end{cases} \\ \text{Then:} \\ T=3\cdot13-1=39-1=38 \\ T=38 \end{gathered}`

Now we can replace T in the second equation:

`\begin{gathered} \begin{cases}T=38 \\ J=T-28\end{cases} \\ \text{Then:} \\ J=38-28=10 \\ J=10 \end{gathered}`

Finally, we can replace J in the first equation to get the age of Mary:

`\begin{gathered} \begin{cases}J=10 \\ M=J+5\end{cases} \\ \text{Then:} \\ M=10+5=15 \end{gathered}`

Thus, the age of Mary is 15 years old.