Question

13. Nick is five years older than Will. The sum of their ages is 21. How old is Nick? Solve algebraically.

Answer 1

Nick = 13 years old.

Explanation:

Define the variables:

• Let n = the age of Nick (in years).
• Let w = the age of Will (in years).

Given:

• Nick is 5 years older than Will.
• The sum of their ages is 21.

Create a system of equations with the given information and defined variables:

`\begin{cases} w=n-5\\n+w=21\end{cases}`

Substitute the first equation into the second equation and solve for n:

`\implies n+(n-5)=21`

`\implies 2n-5=21`

`\implies 2n-5+5=21+5`

`\implies 2n=26`

`\implies 2n / 2=26 / 2`

`\implies n=13`

Therefore, Nick is 13 years old.

To find the age of Will, simply substitute the found value of n into the first equation and solve for w:

`\implies w=13-5`

`\implies w=8`

Therefore, Will is 8 years old.