The equation that describes the cost depending on the number of jerseys from each company, is:
[tex]\begin{gathered} \text{Guy's Graphix}\rightarrow y=7.5x+30 \\ \text{Patty's Printing}\rightarrow y=5.5x+50 \\ \text{Sherman Shirts}\rightarrow y=8x+20 \end{gathered}[/tex]Evaluate each equation in the given number of jerseys to find which one is cheaper depending on the number of jerseys:
8 jerseys
[tex]\begin{gathered} \text{Guy's Graphix}\rightarrow y=7.5(8)+30=90 \\ \text{Patty's Printing}\rightarrow y=5.5(8)+50=94 \\ \text{Sherman Shirts}\rightarrow y=8(8)+20=84 \end{gathered}[/tex]The cheapest option is Sherman Shirts.
13 jerseys
[tex]\begin{gathered} \text{Guy's Graphix}\rightarrow y=7.5(13)+30=127.5 \\ \text{Patty's Printing}\rightarrow y=5.5(13)+50=121.5 \\ \text{Sherman Shirts}\rightarrow y=8(13)+20=124 \end{gathered}[/tex]The cheapest option is Patty's Printing.
3 jerseys
[tex]\begin{gathered} \text{Guy's Graphix}\rightarrow y=7.5(3)+30=52.5 \\ \text{Patty's Printing}\rightarrow y=5.5(3)+50=66.5 \\ \text{Sherman Shirts}\rightarrow y=8(13)+20=44 \end{gathered}[/tex]The cheapest option is Sherman Shirts.
10 jerseys
[tex]\begin{gathered} \text{Guy's Graphix}\rightarrow y=7.5(10)+30=105 \\ \text{Patty's Printing}\rightarrow y=5.5(10)+50=105 \\ \text{Sherman Shirts}\rightarrow y=8(10)+20=100 \end{gathered}[/tex]The cheapest option is Sherman Shirts.
12 jerseys
[tex]\begin{gathered} \text{Guy's Graphix}\rightarrow y=7.5(12)+30=120 \\ \text{Patty's Printing}\rightarrow y=5.5(12)+50=116 \\ \text{Sherman Shirts}\rightarrow y=8(12)+20=116 \end{gathered}[/tex]The cheapest options are Patty's Printing and Sherman Shirts.
18 jerseys
[tex]\begin{gathered} \text{Guy's Graphix}\rightarrow y=7.5(18)+30=165 \\ \text{Patty's Printing}\rightarrow y=5.5(18)+50=149 \\ \text{Sherman Shirts}\rightarrow y=8(18)+20=164 \end{gathered}[/tex]The cheapest option is Patty's Printing.
