Question

Kyile is ready to place an order with Patty's printing when he hears that a new company has recently opened in town. Sherman Shirts charges 20 to create the artwork for team logo plus $8 per jerseys. which company has a lower total cost for different numbers of jerseys

Answer 1

The equation that describes the cost depending on the number of jerseys from each company, is:

`\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}`

Evaluate each equation in the given number of jerseys to find which one is cheaper depending on the number of jerseys:

8 jerseys

`\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}`

The cheapest option is Sherman Shirts.

13 jerseys

`\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}`

The cheapest option is Patty's Printing.

3 jerseys

`\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}`

The cheapest option is Sherman Shirts.

10 jerseys

`\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}`

The cheapest option is Sherman Shirts.

12 jerseys

`\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}`

The cheapest options are Patty's Printing and Sherman Shirts.

18 jerseys

`\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}`

The cheapest option is Patty's Printing.