Respuesta :
Answer:
The most he can pay for each of the remaining ladders if he is to obtain a 48% markup goal is $36.357.
Explanation:
- A hardware buyer plans to purchase 75 ladders which will retail for $35 each. This means that he is going to sell each ladder for $35, regardless of how much he paid for them before.
- He has already placed an order for 48 ladders at $16.50 each. So out of the 75 ladders he is planning to purchase and then sell, he bought 48 at a reduced price of only $16.50 each. Now if we subtract those numbers, as shown below, we determine that he still needs to buy 27 more ladders at an unknown price:
(75 - 48) ladders = 27 ladders
- What is the most he can pay for each of the remaining ladders if he is to obtain a 48% markup goal? So we need to determine the maximum price for each of the remaining 27 ladders if he is to obtain a 48% markup goal.
Markup in this case is just a measure of the ratio (in %) between the profit made (by selling 75 ladders for $35 each) to the cost paid (by buying 48 of them at $16.5 each and 27 of them at an unknown price). Its formula is as follows:
[tex]Markup=\frac{Profit}{Cost}*100[/tex]
Now, we already have our markup goal of 48%, so we can substitute that number into the formula, and divide both sides of the equation by 100:
[tex]48=\frac{Profit}{Cost}*100\\0.48=\frac{Profit}{Cost}\\\frac{Profit}{Cost}=0.48[/tex]
We know that Cost is the sum of what he paid for the 48 ladders, plus what he is to pay for the remaining 27 ladders, so it should look something like this:
[tex]Cost=(48ladders*16.5\frac{dollars}{ladder} )+(27ladders*x)[/tex]
[tex]Cost=(792 dollars)+(27ladders*x)[/tex]
Where 'x' is the maximum price he can pay for each of the remaining 27 ladders if he is to obtain a 48% markup goal.
We should also know that Profit is what he gets by selling the 75 ladders, minus the cost paid for them. It should look something like this:
[tex]Profit=(75ladders*35\frac{dollars}{ladder} )-[(792dollars)+(27ladders*x)][/tex]
[tex]Profit=(2625dollars)-[(792dollars)+(27ladders*x)]\\Profit=(2625dollars)-(792dollars)-(27ladders*x)\\Profit=(1833dollars)-(27ladders*x)[/tex]
Next, we want to substitute what we have so far for Cost and Profit into the worked Markup formula we had written before, and solve the equation by isolating our 'x'. To do that, let's follow these steps:
[tex]\frac{Profit}{Cost}=0.48[/tex]
[tex]\frac{(1833dollars)-(27ladders*x)}{(792 dollars)+(27ladders*x)}=0.48\\1833dollars-27ladders*x=0.48*[792 dollars+27ladders*x]\\1833dollars-27ladders*x=380.16dollars+12.96ladders*x[/tex]
At this point, we want to transfer the 'x' terms to one side of the equation, and the other terms to the other side, so we get to the answer:
[tex]1833dollars-380.16dollars=12.96ladders*x+27ladders*x\\1452.84dollars=(12.96+27)ladders*x\\1452.84dollars=39.96ladders*x[/tex]
Finally, we divide both sides of the equation by 39.96 ladders:
[tex]\frac{1452.84dollars}{39.96ladders} =x\\36.357\frac{dollars}{ladders}=x\\x=36.357\frac{dollars}{ladders}[/tex]
So the most he can pay for each of the remaining ladders if he is to obtain a 48% markup goal is $36.357. That means that even if he buys the remaining ladders for a higher price than what he is willing to sell them for, he still obtains a 48% markup goal.
