systems of linear equations

Question

Hello my name is Garrett and i wanted to ask you about this question

Ms. Wade was offered two different sales jobs. For the first job, she would earn a base salary of $500 per week plus a 6% sales commission. for the second job, she would earn a base salary of $350 per week plus 10% sales commission.

1. write a system of equations in two variables to model this situation
2. What amount in weekly sales will yield the same weekly salary for both jobs? justify your answer mathematically.
3. How could this information help ms. Wade decide which job she should accept

Answer 1

Let x equal the weekly salary Ms. Wade could earn at Job 1.

x = 500 + 0.06s

Where 500 is the base salary and the variable 's' is sales. To find out how much commission Ms. Wade makes, we convert 6% into a decimal form, multiply by sales, and add to the base salary.

Similarly, let y be the weekly salary Ms. Wade could earn at Job 2.

y = 350 + 0.1s

In order to determine what amount in weekly sales will yield the same salary for both jobs, simply set these two questions equal to each other and solve for 's'.

x = y

500 + 0.06s = 350 + 0.1s

150 + 0.06s = 0.1s

150 = 0.04s

s = 3,750

In other words, Job 1 and Job 2 will have the same weekly salary if Ms. Wade's weekly sales are $3,750. In order to use this information to help her decide which job to accept, Ms. Wade should decide how much weekly sales is realistic for her to accomplish. If she can sell more than $3,750 per week, she should accept Job 2. If she is more likely to sell less than $3,750 in most weeks, she should accept Job 1.