Question

3. Aries was in NYC over the summer watching bikers and runners training for the NYC triathlon. She observed that there were 178 more runners than bikers. If there were a total of 676 people in the park, how many people were running and how many people were biking?

Answer 1

To solve this problem we can express one equation for each condition so the first ones is:

There are 178 more runners than bikers so:

$R=B+178$

whre R are the runners and B are the bikers

and the second one is:

in total there are 676 people this means that:

$R+B=676$

now we can replace the first equation into the second one so we have:

$\begin{gathered} B+178+B=676 \\ 2B=676-178 \\ B=\frac{498}{2} \\ B=249 \end{gathered}$

now we can replace B in the first equation so:

$\begin{gathered} R=249+178 \\ R=427 \end{gathered}$

So in total the there are 427 runners and 249 bikers