A department store worker can earn $500 per month plus a 4% commission on their total sales, or $400 a month plus a commission on total sales.

Question

Kenisha sells athletic shoes part-time at department store. She can earn either $500 per month plus a 4% commission on her total sales, or $400 a month plus a 5% commission on total sales. Write a system of linear equations to represent the situation, then calculate the total price of the athletic shoes Kenisha needs to sell in order to earn the same income from each pay scale. Which is the better offer?

Answer 1

y₁ = 500 + .04x

y₂ = 400 + .05x

 

500 + .04x = 400 + .05x  Subtract 400 from each side of the equation.

 

100 + .04x = .05x  Subtract .04x from each side of the equation.

 

100 = .01x  Divide both sides of the equation by .01.

 

10,000 = x  Kenisha needs to sell $10,000 of athletic shoes for the two pay plans to pay the same amount.

 

For sales under $10,000, the $500 base plan is the better plan. For sales over $10,00, the $400 base plan will result in a larger paycheck.