Question

mandi is paid $100 a week plus $10 for each new cell phone plan she sells. she may switch to a new company that pays $80 a week but $15 for each plan she sells. how many memberships per week does mandi need to sell for the new company to be a better deal for her? justify the response with mathematical reasoning and/or calculations.

Answer 1

Mandi needs to sell more than 4 memberships per week for the new company to be a better deal.

Step-by-step explanation:

Given that Mandi is paid $100 a week plus $10 for each new cell phone plan she sells, let x be the number of new cell phone plan she sells, then

100 + 10x

is the expression for her earning.

She may switch to a new company that pays $80 a week but $15 for each plans she sells, her earnings is written as

80 + 15x

If the new company must be a better deal, then her earnings, then her earnings in the new company must be greater than her earnings in the old one.

80 + 15x > 100 + 10x

Solving the inequality above, we have the number of memberships per week she requires for the deal.

Subtract 10x from both sides of the inequality

80 + 15x - 10x > 100 + 10x - 10x

80 + 5x > 100

Subtract 80 from both sides

80 + 5x - 80 > 100 - 80

5x > 20

Divide both sides by 5

5x/5 > 20/5

x > 4

The number of memberships Mandi needs is greater than 4.