Rlee R.

asked • 03/27/17

guys i need your help. please

guys i need your help. please
 
Cora is buying chairs and tables to complete her party supplies room inventory. She made two visits to the furniture store. During her first visit, she bought 10 chairs and 4 tables and paid 2900 pesos. In her last visit, she bought 26 chairs and 5 tables and paid 5650 pesos. How much is a chair and a table?

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Cristina S. answered • 03/27/17

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set up equations with the info given:
 
10c+4t=2900   (*-1)
26c+5t=5650
--------------------
add after multiplying first equation by -1.

16c+t=2750

So, t=2750-16c, now substitute this value of t in one of the equations above to get c; then substitute c value in this t equation to get t

After you have t and c, all you have to do is calculate c+t to get the cost of a chair and a table.
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Rlee R.

i substituted the t=2750-16c. i got an answer of Chair-4400, Table-8800. im still wrong. please help
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03/27/17

Tim C.

tutor
I will assume Cristina is probably in bed now and help out :)
 
Substitute it in either equation.  Let's pick the first:
 
10c + 4(2750-16c) = 2900  -->
 
   10c + 11000 -64c = 2900 --->
   
         -54c + 11000 = 2900 -->
  
             -54c = -8100  -->
 
                 c = 150
 
You should be able to substitute "c" back into either equation to figure out "t".
 
 
 
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03/27/17

Cristina S.

Rlee,

You must watch your signs, you can't get negative chairs and negative tables :)

Substitute for t in the first equation:

10c+4(2750-16c)=2900

10c+4*2750-4*16c=2900
 
10c-64c=2900-4*2750
You are not going to get negative chairs if you solve it correctly.  Try again and post if you are still having problems.  If I solve it for you, you won't learn
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03/27/17

Rlee R.

Thank you for making me learn by myself, but i need a quick answer madam, i'm about to go crazy with all of these. :(
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03/28/17

Cristina S.

Ok, I will do it slowly, so hopefully you learn something:
 
work each side of the equation:

10c-64c= -54c
 
2900-4*2750=-8100

Now you have: -54c=-8100

Divide both sides by -54:

c=150 (not negative 150, if you divide a negative number by another negative number, the result is a positive number!)

Now substitute c=150 in t=2750-16c

I think you can do this, there isn't much you can do to mess it up :)  Then add your c=150 to whatever t you get, and that will be your answer :)  Post again if you still don't get it, I have to do something else now, but I'll take a look in a few minutes
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03/28/17

Rlee R.

Lets forget that question madam, this one is my new problem. i need a quick answer madam i will learn it after you give me a answer. I'm sorry for bothering you i know you very busy.
 
The sum of the digits of a three-digit number is 17. The tens digit is 12 less than the sum of the units digit and twice the hundreds digit. If the units digit and the hundreds digit are reversed, the new number is 297 less than the original number. What is the original number?
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03/28/17

Cristina S.

There are no quick answers with this type of problems for neither of us, unless we use a computer program of some sort. You have to manipulate the equations to get the answers.  The more you practice, the faster you will be able to see what possible manipulations you can use to solve them.  Did you at least set the equations up?
 
these should be your equations:
x+y+z=17
y=(z+2*x)-12
zyx=xyz-297----this is a little tricky and you should think of it as how the digits should relate algebraically in order to use it: z*100+y*10+x=x*100+y*10+z-297 
 
So you have 3 equations with 3 unknowns.  Do some work and submit it and I'll take a look of it, if you want.  You won't learn how to manipulate equations if someone is doing it for you.
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03/28/17

Rlee R.

Thank you very much Madam for putting effort to assist me , I will do my best to learn Quadratic, Polynomial Equations, I think that's what i need to learn first to answer this word problem. I will tell you my progress and hopefully you would help me again. Thank you very much and God Bless. :)
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03/28/17

Cristina S.

Rlee,

I will submit the answer for you shortly, but I have to do something else first.  I wanted you to try it so that you learn.  This doesn't have anything to do with quadratics, it should be much easier than that.  All of us leaned by doing it ourselves.  Go back to basic linear equations and learn them or you will always have problems with these problems and much harder ones to come.  There is no easy way out.  I'll be back in about 1/2 h.
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03/28/17

Cristina S.


 
The sum of the digits of a three-digit number is 17. The tens digit is 12 less than the sum of the units digit and twice the hundreds digit. If the units digit and the hundreds digit are reversed, the new number is 297 less than the original number. What is the original number?

x+y+z=17
y=(z+2*x)-12
zyx=xyz-297


x+y+z=17
-2x+y-z=-12
___________add to eliminate z

-x+2y=5, so x=2y-5

Now work on this and substitute the x above:
zyx=xyz-297

z*100+y*10+x=x*100+y*10+z-297

you can cancel 10y on both sides

100z+x=100x+z-297
99z-99x=-297, or

99x-99z=297; divide by 99
--------------------
x-z=3 nice! , so x=z+3 and from above, x=2y-5, so
 
z+3 =2y-5, add -3
z=2y-8

substitute z in first eq
2y-5+y+2y-8=17
5y=30, y=6

Now substitute y=6 in previous equation z=2y-8
z=12-8, so z=4

Substitute z in previous equation x=3+z
x=3+4=7

The number is xyz=764

Lets Check:

764-297=467

As you can see, there is not quick answer, I had to do some work too.  There are many ways to  solve these problems but they take some time and effort.  Not terribly difficult, but they require you master previous skills.

Best of luck!

























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03/28/17

Cristina S.


 
The sum of the digits of a three-digit number is 17. The tens digit is 12 less than the sum of the units digit and twice the hundreds digit. If the units digit and the hundreds digit are reversed, the new number is 297 less than the original number. What is the original number?

x+y+z=17
y=(z+2*x)-12
zyx=xyz-297
 
I start here working on the first 2 equations, but there are many ways to solve this.
x+y+z=17
y=(z+2*x)-12
--------------------

x+y+z=17
-2x+y-z=-12
___________add to eliminate z

-x+2y=5   Multiply by -1
 
x=2y-5  Call this expression (1)

Now work on this and substitute the x above:
zyx=xyz-297

z*100+y*10+x=x*100+y*10+z-297

you can cancel 10y on both sides

100z+x=100x+z-297
99z-99x=-297    multiply by -1

99x-99z=297; divide by 99
--------------------
x-z=3   nice!  add z
 
so x=z+3,   Call this expression (2)
 
or z=x-3

But from expression (1) above, x=2y-5, so z=2y-5-3=2y-8

substitute in first eq
2y-5+y+2y-8=17
5y=30, y=6

Substituting in one of simple equations:

z=12-8 or z=4   Expression (4)

Recall expression(2)  and substitute z from expression (4)
x=3+z=3+4=7

Check your answer:
The number is xyz=764

764-297=467  it works!
 
 
 
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03/28/17

Cristina S.

Rlee:
I can't post the answer to your second problem, maybe because comments can't be very long? I don't know! Repost the second problem in a new post and I will post the answer. I hope you will study the steps and learn from it.
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03/28/17

Rlee R.

Cristina S:
Thank you for this answer! I will study my lessons at its depth. I'll get back to you soon as i could.
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03/28/17

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