Question

9. Joanna is considering two job offers. Phoenix Fashions offers

$1500/month plus 2.5% commission. Styles by Rebecca offers

$1250/month plus 5.5% commission.

a) Create a linear system by writing an equation for each salary.

b) What value of sales would result in the same total salary

for both jobs?

c) Which job should Joanna take? Explain your answer.

Answer 1

To solve Joanna's job offer dilemma, linear equations for each job's salary were formed and the break-even sales point was calculated as $8,333.33. Joanna should choose Phoenix Fashions for sales below this point and Styles by Rebecca for sales above it.

Step-by-step explanation:

Linear Systems Representing Salary Offers

To address Joanna's decision between two job offers, we'll create two equations representing each salary offer:

• Phoenix Fashions: S1 = 1500 + 0.025x where S1 is the total salary from Phoenix Fashions and x is the amount of sales made.
• Styles by Rebecca: S2 = 1250 + 0.055x where S2 is the total salary from Styles by Rebecca and x is the amount of sales made.

Equating Salary for Equal Sales

To find the value of sales that would result in the same total salary (break-even point) for both jobs, we set S1 equal to S2 and solve for x:

1500 + 0.025x = 1250 + 0.055x
250 = 0.03x
x = 250 / 0.03
x = 8333.33

So, Joanna would need to make $8,333.33 in sales to earn the same salary from both jobs.

Job Selection

Joanna should choose the job that would give her the highest salary depending on her expected sales. If she expects sales to be below $8,333.33, then Phoenix Fashions would be the better choice. If she expects her sales to exceed this amount, Styles by Rebecca would offer a higher salary due to the higher commission rate.

Answer 2

A] 1500 + 0.025x , 1250 + 0.055x ; B] Sales value = 8333

C] Offer 1, if prefers more fix salary over additional incentive. And, offer 2 if prefers additional incentive over fix salary.

Step-by-step explanation:

Let the sales be = x

A] Offer 1 = 1500 + 2.5% comm on sales = 1500 + 2.5%x = 1500 + 0.025x

Offer 2 = 1250 + 5.5% comm on sales = 1250 + 5.5%x = 1250 + 0.055x

B] Value of sales, resulting in total salary : at equation 1 = equation 2

1500 + 0.025x = 1250 + 0.055x

1500 - 1250 = 0.055x - 0.025x → 250 = 0.03x

x = 250 / 0.03 → x (Sales value) = 8333

C] Which job she should take, would depend on her preferences.

If she wants more fixed salary, & less above per unit achievement, she should take offer 1 as fixed salary 1500 > 1250. If she wants less fixed salary & more additional incentives, she should take offer 2, as commission 5.5% > 2.5%