In a "seven-eleven" (7-11) store, a customer selected four items to buy. The check-out clerk says that he multiplied the costs of the items and obtained exactly 7.11, the very name of the store! The customer calmly tells the clerk that the costs of the items should be added, not multiplied. The clerk then informs the customer that the correct total is also $7.11.
What are the exact costs of the 4 items?

HERE IS THE HOMEWORK:
Using what you know about the associative properties of addition and multiplication:
a.) Describe a method finding four prices using a system of equations.

b. ) Solving your system by graphing and by substitution.


This is sooo terrible! It's my son's 9th grade, Adv. Integrated Math 2 problem and the answer counts as two quiz grades. We've been trying at it all day and can't get it. We've found the "answer" to the problem online, but we STILL can't answer a. & b.. Please, help!!!! Don't use any sales tax.

All I know is system of equations are:
w+x+y+z=$7.11
w*x*y*z=$7.11
Here's a link to the "answer":
http://www.pen.k12.va.us/Div/Winches...4/a053104.html

I have gone through it and still CAN'T HELP ANSWER his homework!!!!
HELP (if you can)!!!!!

We are given:

w + x + y + z = 7.11 AND
w * x * y * z = 7.11, as you suggested.

Now, if we convert them both into cents, we have the following:

w + x + y + z = 7.11
w * x * y * z = 711000000

However, if you factor 711000000, you get:

2^6*3^2*5^6*79;

Out of our variables w, x, y and z, only one will be a multiple of 79.

I don't have time to complete the problem now, but what you will need to do is go through the cases of which amount is a multiple of 79 and then find unique solutions to which satisfy your equation you come up with.

Nice problem.

I'll complete it later if no-one has helped you by then.

HERE IS THE HOMEWORK:
Using what you know about the associative properties of addition and multiplication:
a.) Describe a method finding four prices using a system of equations.
Would it be considered the Substitution Method?
b. ) Solve your system by graphing and by substitution.
How could this be solved by graphing???

Please post new problems in new threads. See the rules, #14.

-Dan

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"I must not fear. Fear is the mind killer. Fear is the little death that brings total obliteration. I will face my fear. I will permit it to pass over me and through me. And when it has gone I will turn the inner eye to see its path. Where the fear has gone there will be nothing. Only I will remain." - The Litany Against Fear, "Dune" by Frank Herbert

I think the second post was on the same question, although it just repeated the original post.

I feel silly now... Sorry!

-Dan

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"I must not fear. Fear is the mind killer. Fear is the little death that brings total obliteration. I will face my fear. I will permit it to pass over me and through me. And when it has gone I will turn the inner eye to see its path. Where the fear has gone there will be nothing. Only I will remain." - The Litany Against Fear, "Dune" by Frank Herbert

I'm still on the original equation. Today, the whole class had answers based on what is shown online (convert to cents, find #'s divisible by 79, etc.). The teacher said she didn't want it done that way. She wants everyone to use the Substitution Method that is normally worked with in High School Algebra to find the solution. Is that even possible???!!! She also said to use the Quadratic Equation to graph. How? This is what she showed the class today to get started on solving the 9-11 equation (original post):

a+b+c+d = 7.11 and abcd = 7.11
converted to:
(a+b)+(c+d) = 7.11 and (ab)(cd) = 7.11

x+y = 7.11 and xy = 7.11

Do you get anything from this? Is there a way to answer the 7-11 problem using high school Algebra? I'm getting the idea that this teacher doesn't know what she's doing and can't answer the problem herself! Either that, or she's the world foremost math genious. What should I do about this assignment that counts as the END OF QUARTER PROJECT??? Can anyone give me anything to help me put something down on paper???

Thanks!!!!

I presume that somewhere in here is the required assumption that a, b, c, and d are all expressible in terms of a whole number of cents. I don't know why your teacher would object to that method.

I'm not sure what to say. Your teacher is suggesting that we can set
x = a + b = a*b
y = c + d = c*d
(This is similar to the original problem: that the sum of a series of numbers is equal to the product of that same series.) This (assumption?) COULD happen, but I see no reason that it HAS to happen. (See the end of this post. I showed that it is NOT true.)

If this does happen, then:
x + y = 7.11
xy = 7.11

From the first equation:
y = 7.11 - x
Inserting this into the second equation:
x(7.11 - x) = 7.11

7.11x - x^2 = 7.11
0 = x^2 -7.11x + 7.11

From the quadratic formula:
x = 5.906175238 or x = 1.203824762

Thus: y = 7.11 - x:
y = 1.203824762 or y = 5.906175238

So it doesn't matter which solution we pick for x.

The problem I have with this is that neither value for x is expressible to an exact number of cents.

But, moving blindly on:
x = a + b = a*b
So let x = 5.906175238.
5.906175238 = a + b
5.906175238 = a*b

So from the first equation b = 5.906175238 - a
So
5.906175238 = a(5.906175238 - a)

Just like we found x and y.
I get:
a = 4.63075
b = 1.27543

But when I set up the c, d equations I get imaginary solutions. So the assumption that
x = a + b = a*b
y = c + d = c*d
is apparently wrong.

-Dan

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"I must not fear. Fear is the mind killer. Fear is the little death that brings total obliteration. I will face my fear. I will permit it to pass over me and through me. And when it has gone I will turn the inner eye to see its path. Where the fear has gone there will be nothing. Only I will remain." - The Litany Against Fear, "Dune" by Frank Herbert

Dan,
Thank you for proving this. I was just working on it that way myself. I didn't think it could give the right answers though. After all, wouldn't the mathematicians being doing it this way, since it's easier, if that is all it took?! I'm guessing the teacher didn't really look hard enough at this problem when she assigned it for the Quarter Project. Would you agree?
Thanks again!

She may have thought she had a short cut. There may indeed be something to it (I didn't do the graphs myself, there may be something there.) However, there is nothing wrong with the problem itself, just her approach.

I would suggest you finish out what I was working on and show her that c and d are complex numbers. See what she says. (Given the way today is going for me I might have made a mistake in my work, so don't take my word for it! )

-Dan

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"I must not fear. Fear is the mind killer. Fear is the little death that brings total obliteration. I will face my fear. I will permit it to pass over me and through me. And when it has gone I will turn the inner eye to see its path. Where the fear has gone there will be nothing. Only I will remain." - The Litany Against Fear, "Dune" by Frank Herbert