Kenisha sells athletic shoes part-time at a department store. She can earn either $500 per month plus a 4% commission on her total sales, or $400 per month plus a 5% commission on total sales.
Write a system of equations to represent the situation.
What is the total price of the athletic shoes Kenisha needs to sell to earn the same income from each pay scale?
Which is the better offer?
I answered this question previously. However, here it is again.
$500 + .04x = $400 + .05x
x will give you the amount she has to sell to get the same income.
The better offer depends on how good a salesperson she is, how much she expects to sell.
I hope this helps again. Thanks for asking.
This didn’t answer all parts of the question.
To represent Kenisha's situation, we can use a system of equations.
Let's denote the total sales as 'S' and the total income as 'I'.
For the first pay scale, Kenisha earns $500 per month plus a 4% commission on her total sales:
Income (I) = $500 + 0.04S
For the second pay scale, Kenisha earns $400 per month plus a 5% commission on her total sales:
Income (I) = $400 + 0.05S
Now, to find the total price of athletic shoes Kenisha needs to sell to earn the same income from each pay scale, we need to set the two equations equal to each other and solve for 'S':
$500 + 0.04S = $400 + 0.05S
Subtracting 0.04S and $400 from both sides:
$100 = 0.01S
Dividing both sides by 0.01:
S = $10,000
Therefore, Kenisha needs to sell a total of $10,000 worth of athletic shoes to earn the same income from each pay scale.
To determine which offer is better, we can compare the incomes for different levels of sales. Let's compare the incomes when Kenisha sells $5,000 worth of athletic shoes.
For the first pay scale:
Income = $500 + 0.04($5,000) = $500 + $200 = $700
For the second pay scale:
Income = $400 + 0.05($5,000) = $400 + $250 = $650
Comparing the two incomes, we can see that the first pay scale offers a higher income for selling $5,000 worth of athletic shoes.
Therefore, the better offer for Kenisha is the first pay scale, where she earns $500 per month plus a 4% commission on her total sales.