How do you solve this question?

Question

John brought an MP3 player for $240. Given that he offred a 28% discount on the selling price and still made a 20% profit, find the selling price of the MP3 player.

Answer 1

Hi,

If I understand this correctly, John bought an MP3 player for $240. He then increased the price to sell it. From that "selling price" of the MP3 player, he gave a 28% discount during a sale and still made himself a 20% profit.

If that is correct, then in order for him to make a 20% profit on the money he spent for it, John would have to get 120% of 240, which is 1.2 x 240 = $288. This is the "for-sale" price that was paid.

That $288 was after a 28% discount, so the buyer really only paid 72% of the original selling price. If the original selling price was x, then the sales price 288 = .72x. Solving this for x, gives us the selling price of $400 for the MP3 player.

I hope this helps!! :-)

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Now I'm going to type you something entirely unrelated to this problem. I answered another of your problems and you wanted to know how to use STAT on the graphing calculator. I wrote you back a comment, explaining it in great detail, only to have it disappear when I got the system note that there was a 300 character limit that I far exceeded. So in order to be able to explain how to use STAT as you had asked, I am going to type my answer below.

To use STAT on the TI83, press [STAT], [EDIT]. If there is already data in the L1 and L2 lists, move the highlight up on the name L1 and press "clear". When you move back down onto the list in L1, it will disappear. Move over and highlight the name L2 and press "clear". When you move back down onto the list in L2, it will disappear.

Now enter 1,2,3,and 4 in L1 to represent your first, second, third, and fourth terms. Enter 8,4,1,1/3 into L2 beside them.

If you want to graph these points, go to window and make sure your max and min values are large enough to see your points. Then go to [2nd].[Y=] to StatPlot and go to plot 1. Press Enter and turn it on. This will graph your points using x and y values stored in L1 and L2.

To get the equation of your sequence, press [STAT} and move over to [CALC]. Starting at #4, you will see different types of equations you can use to find the line of best fit. The way you can tell for sure which is best is to first go to [2nd], [0] to get to CATALOG. Scroll down to DiagnosticOn and press ENTER twice. This turns on the "r" value for you which evaluates how well the equation fits to the points. A perfect fit will be either r = -1 or 1, which is also r² = 1. The closer r is to zero, the more inaccurate the equation is.

Anyhow, to get the equation of your sequence, press [STAT} and move over to [CALC]. Starting at #4, you will see different types of equations you can use to find the line of best fit. LinReg is for a straight line and requires a minimum of 2 points. QuadReg is for a parabola and requires a minimum of 3 points. CubicReg is for a cubic equation and requires a minimum of 4 points. This is what you had. (Quartic would need at least 5 points) There are others below that might also work for certain data like LnReg, ExpReg, PwrReg,Logistic, and SinReg. Use these only if you are not getting a high enough "r" value.

To get your equation entered into your calculator so you can see its graph and look at its values in the table, choose your equation type and press ENTER. For yours, I used CubicReg.

On your screen you'll see:
CubicReg

Type [2nd],[0] to get CubicReg L1
Type a comma above the [7]. Now you have:
CubicReg L1,

Type [2nd],[1] to get CubicReg L1, L2
Type a comma above the [7]. Now you have:
CubicReg L1, L2,

Now press [VARS] , move over to Y-VARS, select FUNCTION, and Y1. Now you have:
CubicReg L1, L2, Y1

When you hit enter your equation will be stored under Y= and if you hit graph you will see its relation to your points. To see the data to find more points, press [2nd], [GRAPH] to get to TABLE. Scroll down to find terms 5,6,etc.

When you are done with this, be SURE to go back into STATPLOT and turn the STATPLOT off. Otherwise it will screw up other graphs and keep your calculator from working.

I hope that helps you!! :-)

Answer 2

Well it seems like he paid $240.00 for it thats including the 28% that was discounted. So the 28% is extraneous information that is included in the problem to confuse you.

Now people here will tell you to just subtract 20% to find out how much he paid for the MP3 Player but thats not true. The seller gained 20% profit and thats based on the actual cost of the MP3 player. Its like this.... I bought a pair of shoes for $100.00, I sold it for $130.00 so Its clear that I made a 30% profit. But when you take away 30% off the price he paid for it you get $91.00 which is not how much I paid for it.

So what you really do is this.....

Actual Cost * 1.20 = How much he paid for it.....

So let X be the actual cost....

1.20X = $240.00

So divide 1.20 from $240.00 and you get....$200.00

Thats how much the MP3 Player really cost.

But hm...... the question is asking "find the selling price of the MP3 Player"

That means how much is the original price of the mp3 player before the 28% discount. Now the profit has nothing to do with it.


So the answer will be like this.....

If its asking for the retail price of the MP3 player then it will be 28% less than $240.00

So let X be actual retail price.... this is different from cost btw.

X - 28% = $240.00

So what you can do is..... set an equation.....

X - (.28X) = $240.00

and X should be equal to $333.33333

Answer 3

Let John sell it for $ x

Abbreviations used:
SP = Selling Price (No discount)
ASP = Actual Selling Price
CP = Cost Price
P = Profit
P% = Profit %

Solution:

P% = (P/CP) * 100
20 = 100P/CP
20CP = 100P
20 * 240 = 100P
P = $ 48

ASP = 240 + 40 = $288

ASP = [(100 - 28)/100] * SP
288 = 72*SP/100
72*SP = 28800
SP = 28800/72
SP = 400

So, the Sale Price of the MP3, without discount is $400

Answer 4

It's only asking you for the selling price. Having already told you that he made a 20percent profit, that would mean that you only need to know what 20pct of the original cost was and add it to the original cost. The discount is just to confuse you.

Answer 5

mp3's original cost? ok, $240 less 28% gives us $172.80 (this is the discounted prices). to compute for the orig price plus the 20% profit, let's assume;
x=orig price
0.20x=profit

therefore, x + 0.20x = 172.80, solving for x
$144 = orig price of mp3 player

Answer 6

find the 28% of the cost price. subtract it. you have the actual cost price. also you have the profit %.
profit % = (profit/Cost price)*100