Question

For what amount of Chris better off selecting plan A?

Answer 1

Chris is better off selecting plan A when greater than 5500

Explanation:

Payment plan A:

Salary = $480

Commission = 8%

let the slaes price = m

$\begin{gathered} Co\text{mmission = sales price}\times\text{ 8\% =m }\times\text{ 0.08} \\ T\text{otal amount to be received per month = 480 + 0.08m} \end{gathered}$

Payment Plan B:

Salary = $755

Commision = 3%

$\begin{gathered} \text{Commission amount = sales price }\times\text{ 3\% = m }\times\text{ 0.03 = 0.03m} \\ \text{Total amount to be received per month = }755\text{ +0.03m} \end{gathered}$$\begin{gathered} equating\text{ both equations:} \\ 480\text{ + 0.08m = 755 + 0.03m} \\ 0.08m\text{ -0.03m = 755 - 480} \\ 0.05m\text{ = 275} \\ m\text{ = 275/0}.05 \\ m\text{ = 5}500 \end{gathered}$

When the sales price is $5500, both plans pay the same amount

If plan is greater than 5500. For example: m = 6000

Plan A: 480 + 0.08(6000) = 960

Plan B: 755 + 0.03(6000) = 935

if plan is less than 5500, for example m = 5000

Plan A: 480 + 0.08(5000) = 880

Plan B: 755 + 0.03(5000) = 905

If the sales price is greater than $5500, then plan A is preferable