A caterer is making cookie trays for upcoming holiday parties. This morning, she made 2 small trays and 2 large trays, which contain a total of 112 cookies. In the afternoon, she made 1 small tray and 4 large trays, which contain a total of 173 cookies. How many cookies do the different sized trays contain?.

Answer:Each small tray can contain 17 cookies, while each large tray can contain 39 cookies.Step-by-step explanation:Let's set some variables. [tex]S=[/tex] Small trays, [tex]L=[/tex] Large trays.[tex]\left \{ {{2S+2L=112} \atop {S+4L=173}} \right. \\\\\left \{ {{2S+2L=112} \atop {S=173-4L}} \right. \\\\\left \{ {{2(173-4L)+2L=112} \atop {S=173-4L}} \right.\\\\\left \{ {{346-8L+2L=112} \atop {S=173-4L}} \right\\\\\left \{ {{346-6L=112} \atop {S=173-4L}} \right\\\\\left \{ {{346-112=6L} \atop {S=173-4L}} \right\\\\\left \{ {{234=6L} \atop {S=173-4L}} \right\\\\\left \{ {{39=L} \atop {S=173-4L}} \right\\\\\left \{ {{39=L} \atop {S=173-4(39)}} \right[/tex][tex]\left \{ {{39=L} \atop {S=173-4(39)}} \right\\\\\left \{ {{39=L} \atop {S=173-156}} \right\\\\\left \{ {{39=L} \atop {S=17}} \right[/tex]So each small tray can contain 17 cookies, while each large tray can contain 39 cookies.