Please help! Write a System of two equations in two unknowns

[watcjpp]

My Problem is to be solved by the Subsitution Method.
x+y= $30,000 The total ammount invested is $30,000 and $2,300 has been gain in interest so far. Part of the total amount was invested at 10% and the remainder at 5%.

x=10%
y=5%

0.10x+0.05y=2300
0.10(30,000-y)+0.05y=2300
3000-0.10y+0.05y

and I am stuck here. I would appreciate any assistance that I can recieve.
Thank You,

 

[stapel]

What happened to the right-hand side of your equation? Where'd it go?

Eliz.

 

[watcjpp]

Help

That is what I am unsure of is where do I go from here? I am just stuck.

0.10x+0.05y=2300
0.10(30,000-y)+0.05y=2300
3000-0.10+0.05y=2999.95+0.05=3000

 

[stapel]

I'm sorry, but I have no idea what you're doing. You set the problem up fine, but then your work makes no sense. For instance, how did "0.10(30 000 - y)" become "3000 - 0.1"? What happened to the variable? How did "2300" become "2999.95 + 0.05"?

Please reply with clarification, doing each step separately and explaining what you're doing. Thank you.

Eliz.

 

[watcjpp]

0.10x+0.05y=2300
0.10(30,000-y)+0.05y=2300
3000-0.10+0.05y=2999.95+0.05=3000

0.10 % is the ammount of interest earned for one portion of the 30,000
0.05 % is the other ammount earned for the remainder of the money left.
2300 is the ammount of interest earned already.
30,000 is the amount that was invested in the begining. I am asked to write a system of two equqtions in two unknowns for each system by subsitution. That is why I was inserting 0.10 and 0.05 into the equation trying to solve for y first. I hope this helps because i am really trying to get this and I am not understanding it myself. I appreciate your reply.

 

[stapel]

I'm not asking about your set-up. This part is understandable and looks correct.

I'm asking about your working of the equation:

You have "0.10(30 000 - y)" in one line, and you "simplify" this to get "3000 - 0.1" in the next line. What happened to the variable?

You have "2300" in one line, but "2999.95 + 0.05 = 3000" in the next line. How did twenty-three hundred turn into three thousand?

You need to check your work.

Eliz.

 

[watcjpp]

I appreciate you trying to help me I just am confused on the operations so I am messing it up some how. I know that I replace y in the for x with 0.10 then I am lost.

 

[stapel]

You're not replacing anything. You're multiplying 0.1 and y. The product is not "0.1". And I can see no reason to replace "2300" with "3000".

It might be a good idea to start again from "0.10(30,000 - y) + 0.05y = 2300", and try again, this time doing only one step at a time. There is no "replacing" to do at this point. It's just a linear equation, and you're suppoed to solve it.

Eliz.

 

[watcjpp]

0.10x+0.05y=2300
0.10(30,000-y)+0.05y=2300
3000-0.10y+0.05y =2300
0.02y=300
y= 700
x=1600
That is as far as I have gotten and I am not sure how I got this far? :shock:

 

[stapel]

You were okay through "3000-0.10y+0.05y =2300". But...

How did you get that 0.05y - 0.10y equalled 0.02y? Shouldn't you be getting a negative: -0.05y? (10 - 5 = 5, not 2, so 5 - 10 = -5, not +2.)

How did you subtract 3000 from 2300 and get 300?

Even if "0.02y = 300" had been correct, how did you go from there to "y = 700"?

Where did "x = 1600" come from, since x + y has to equal 30 000?

Please check your work and give your reasoning. Thank you.

Eliz.

 

[Denis]

We ask that you try..well, you sure did try...so let's get ya out of your misery!

0.10x + 0.05y = 2300
0.10(30,000 - y) + 0.05y = 2300
3000 - 0.10y + 0.05y = 2300
That's your work, and correct to this point; don't know why you're having
problems finishing it off, but follow me:

move the 3000 to the right, so you have only the terms with y on left:
-.10y + .05y = 2300 - 3000 ; ok?
-.05y = -700 ; ok?
y = -700 / -.05
y = 14000

Ok? YES, it's that simple!