Please help my daughter with this equation!?

Kenisha sells athletic shoes part time at a departmeent 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. ----------what is the total price of the atheltic shoes kenisha needs to sell to earn the same income frome each pay scale? and which is the better offer? THANKS FOR YOUR HELP

Please help my daughter with this equation!?
Let X be the sales Kenisha need to make, the equation will be


0.04X + 500 = 0.05X = 400


500 - 400 = 0.05X - 0.04X


100 = 0.01X


10000 = X


I think the first offer is better, cause it kind of tough to have $10000 sales per month, you think? Hope this help.
Reply:Set it up like this:





x= $ amount of sales sales





500 + 0.04x = 400 + 0.05x





Then solve:





100 = 0.01x





x = $10,000 a month.





That's a heck of a lot of althletic shoes. I'd go for the $500 a month plan.
Reply:If Kenisha sold 100 pairs of shoes @ $100.00 that is $10,000 in sales. At 4% =$400.00 + $500.00 = $900.00 per month.


If she sold 200 pairs of shoes @ 100.00 that is $10,000 in sales. At 5% =$500.00 + $400.00=$900.00 per month.


Kenisha would be better off taking $500.00 plus 4%
Reply:that is pretty tough. i have no clue and im a junior in highschool.
Reply:is there a reason you cant help your daughter?
Reply:to make the same income she would need to make 10,000 dollars in sales. so the 500 dollars plus 4 percent is the better deal unless she is pulling down some heavy numbers
Reply:K's income = Base + commission


Call the amount of sales S





Case 1: Income = 500 + (0.04)S


Case 2: Income = 400 + (0.05)S





We want to figure out how much sales make these two equal, so, set the equations equal





500 + 0.04S = 400 + 0.05S





Rearrange and solve for S


0.01S = 100


S = $10,000





Hmm, how easily can I sell $10,000 worth of shoes working part time?
Reply:Haha, this one takes me back a couple years. Try setting the two equations equal to eachother with the variable X. Like this:





500+.04x=400+.05x now solve for x.


-400 -400





100+.04x=.05x


-.04x -.04x





100=.01x


/.01 /.01





x=10,000





She would need to sell a total of $10,000 worth of shoes.
Reply:tke 400x.05 or 500x.04 i think this is it but bang a gong!
Reply:A = number of shoes





500 + (0.04 x A) = 400 + (0.05 x A)


500 - 400 = (0.05 x A) - (0.04 x A)


100 = 0.05A - 0.04A


100 = 0.01A


100/0.01 = A


10000 = A





10,000 Shoes


500$ and 4% is better deal (selling 10,000 just to make as much as you would with the other deal, impossible!)
Reply:I would agree with MATTMAN. I have had 5 years experience in Medical Code and Billing and he is right.
Reply:all i culd figure out is i thnk she has to sell 25 pairs in order 4 it to b even bt idk wat price tht comes to i think its like 10000 or sumin--and i thnk the better offer is the $500.....bt im nt sure



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