Question

Use your equation to find the cost of purchasing 300 hamburgers from each company .

Answer 1

Part B: Solving for Isosceles Foods

Isosceles Foods charges $1.10 per burger plus a delivery charge of $52.50

If we were to purchase 300 hamburgers, then

`\begin{gathered} \text{Let }x\text{ be the number of hamburgers,} \\ \\ \text{The equation for Isosceles Foods is} \\ y=1.10x+52.50 \\ \\ \text{Substitute }x=300 \\ y=1.10x+52.50 \\ y=1.10(300)+52.50 \\ y=330+52.50 \\ y=382.50 \end{gathered}`

The cost for 300 burgers for Isosceles Foods is $382.50.

Solve for Scalene Wholesale

Scalene Wholesale charges $1.17 per burger plus a delivery charge of $12.25

Purchasing 300 burgers cost

`\begin{gathered} \text{Let }w\text{ be the number of burgers} \\ \text{The equation for Scalene Wholesale is} \\ z=1.17w+12.25 \\ z=1.17(300)+12.25 \\ z=351+12.25 \\ z=363.25 \end{gathered}`

The cost for 300 burgers for Scalene Wholesale is $363.25

Part C: How many hamburgers would have to be purchased so that the cost would be the same for either company.

Equate the two variables such that the variable for number of hamburgers is equal to x, and the cost is the variable y.

`\begin{gathered} \text{Isosceles Foods}\rightarrow y=1.10x+52.50 \\ \text{Scalene Wholesale}\rightarrow y=1.17x+12.25 \\ \\ y=1.17x+12.25\Leftrightarrow y=1.10x+52.50 \\ 1.17x+12.25=1.10x+52.50 \\ 1.17x-1.10x=52.50-12.25 \\ 0.07x=40.25 \\ (0.07x)/(0.07)=(40.25)/(0.07) \\ \frac{\cancel{0.07}x}{\cancel{0.07}}=575 \\ x=575 \end{gathered}`

Substitute x = 575 for both equations

`\begin{gathered} \text{Isosceles Foods} \\ y=1.10x+52.50 \\ y=1.10(575)+52.50 \\ y=632.50+52.50 \\ y=685 \\ \\ \text{Scalene Wholesale} \\ y=1.17x+12.25 \\ y=1.17(575)+12.25 \\ y=672.75+12.25 \\ y=685 \end{gathered}`

Therefore, 575 hamburgers would have to be purchased so that the cost is the same for either company ($685).

Part D: Cost

As solved above previously, the cost when for both stored when 575 hamburgers are purchased is $685.

Part E: If 1000 hamburgers are purchased, which company is selected.

Substituting x = 1000, to both equation, we can compare which of the two stores have a cheaper cost.

`\begin{gathered} \text{Isosceles Foods} \\ y=1.10x+52.50 \\ y=1.10(1000)+52.50 \\ y=1100+52.50 \\ y=1152.50 \\ \\ \text{Scalene Wholesale} \\ y=1.17x+12.25 \\ y=1.17(1000)+12.25 \\ y=1170+12.25 \\ y=1182.50 \end{gathered}`

Comparing the two when purchasing 1000 burgers, Isosceles Foods cost $1152.50, while Scalene Wholesale costs $1182.50.

Therefore, Isosceles would be a better choice since it is cheaper by $30.