21. In cross-country, the team score is determined by the place each individual runnerfinishes. (For example 1st place is one point, 16th place is 16 points, etc.) In their latestmeet, the boys' cross-country team scored 55 points. If there were five runners on theteam and each runner finished one after another, what places did they each come in?Gina Wilson (All Things Algebra, LLC), 2012-2016

Answer:[tex]9^{th},10^{th},11^{st},12^{th},13^{th}\: places[/tex]Step-by-step explanation:In other words, This problem asks us 5 addends (runners), one after another, whose sum is equal to 55. So let's call the runners  [tex]\left\{\begin{matrix}x&1^{st}runner&(x+1)\:2^{nd}\:runner&&(x+2)\: 3^{rd}runner \\ (x+3)4^{th}\:runner&(x+4)5^{th}runner&&& \end{matrix}\right\\.x+x+1+x+2+x+3+x+4=55\Rightarrow 5x+10=55\Rightarrow 5x=45\Rightarrow x=9\\9^{th},10^{th},11^{st},12^{th},13^{th}\: places[/tex]