# Intermediate Algebra help - page 2

i have this algebra question where i have to combine 15% of a solution with 45% of a solution to form 300ml of a 35% solution. i read examples over and over again, and did the problem over and over... Read More

Okay people. Here's one that I'm stuck on.

formula is:
z=(a-b)/c

z=-1.5
a=75
c=10
What is b?

I was going to have a little go at this,then I saw the minus sign and my brain imploded!!!
Last edit by ayemmeff on Jan 31, '03
2. [QUOTE]Originally posted by John Coxey
[B]SOLUTION: "SYSTEM OF EQUATIONS" PROBLEM <-- LOOK FOR THIS IN INDEX OF YOUR ALGEBRA TEXT

STEP 1: SETUP THE EQUATIONS:
(0.15)X + (0.45)Y = 300(0.35) [TOP EQUATION]
X + Y = 300 [BOT EQUATION]

STEP 2: SIMPLIFY TOP EQUATION:
(0.15)X + (0.45)Y = 105 [TOP EQUATION]
DO NOTHING WITH BOT EQUATION: X + Y = 300 [BOT EQUATION]

STEP 3: DIVIDE TOP EQUATION BY (0.15)
X + 3Y = 700 [TOP EQUATION]
DO NOTHING WITH BOT EQUATION: X + Y = 300 [BOT EQUATION]

STEP 4: MULTIPLE TOP EQUATION BY (-1)
-X + -3Y = -700 [TOP EQUATION]
DO NOTHING WITH BOT EQUATION: X + Y = 300 [BOT EQUATION]

STEP 5: ADD TOP AND BOT EQUATION TOGETHER:
-2Y = -400

STEP 6: DIVIDE BOTH SIDES BY (-2)
Y = 200

STEP 7: SUBSTITUTE "Y=200" INTO EITHER THE BOT OR TOP EQUATION. DOES NOT MATTER WHICH EQUATION YOU USE. I SHOW BOTH JUST AS AN EXERCISE.

[TOP EQUATION]
(0.15)X + (0.45)200 = 300(0.35)
(0.15)X + 90 = 105
(0.15)X = 105 - 90
(0.15)X = 15
X = 100

[BOT EQUATION]
X + 200 = 300
X = 300 - 200
X = 100

STEP 8: PROVE BY LETTING X = 100 & Y = 200 AND SUBSTITUTING INTO EITHER TOP OR BOT EQUATION.

[TOP EQUATION]
(0.15)100 + (0.45)200 = 300(0.35)
15 + 90 = 105
105 = 105 ** IMPORTANT THAT BOTH SIDES ARE SAME ***

YOU NEED 100ml of solution X which is a 15% solution.
YOU NEED 200ml of solution Y which is a 45% solution.

ADD THESE TOGETHER AND YOU GET 300ml of solution Z which is a 35% solution.

3. Have a few minutes this morning:

Given: Z = (A-B) / C Find Value of B:

Step 1: MULTIPLY BOTH SIDES BY C TO GET RID OF FRACTION.

CZ = A-B

Step 2: ADD (-A) TO BOTH SIDES

CZ+(-A) = A-B+(-A)

Step 3: SIMPLIFY EQUATION.

CZ-A = A - B - A

Step 4: CLEAN UP RIGHT SIDE OF EQUATION: NOTE THAT A-A = ZERO.

CZ-A = -B ** DO NOT FORGET MINUS SIGN IN FRONT OF B

Step 5: MULTIPLY BOTH SIDES BY (-1)

(-CZ)+A = B

Step 6: CLEAN UP THE EQUATION

A - CZ = B

B = A - CZ

Check your answer by substituting A - CZ for B in the original
equation.

Z = (A-B)/C

Z = (A-(A-CZ))/C
Z = (A-A+CZ)/C
Z = CZ/C
Z = Z ** BOTH SIDES MUST BE EQUAL.

-----

Value of A: A = B + CZ
Value of B: B = A - CZ
Value of C: C = (A - B) / Z
Value of Z: Z = (A - B) / Z

Again, subtitute any of these into original euqation and you should have both sides being equal.

----

Trick here: Watch negative signs - they are easy to miss on an exam when you are in panick mode.

Another Trick: With these types of problems. Always do the check. You can catch mistakes.

Most Important: You MUST understand how algebra works in order to advance into calculus (if that is your choice). It has tons of every day applications - like figuring out your Miles Per Gallon / etc. So you really really want to know it well.

Please - Don't just study it just to get through the class. You really should understand it.

Regarding Calculus. I don't see it being used at all in the computer software industry -- what I do at least (10 yrs experience). But I do live with Algebra. Use it to space out forms and text fields, buttons, etc on web pages. Can't just eyeball it.

====

Getting back to the above problem:

Trick here: Imagine equation as a see-saw that you MUST
keep balanced at ALL TIMES. Whatever you do to left side of
equation - you MUST do to right side of equation.

Meaning:

If you add a number to one side, then you gotta add it to the other.

If you subtract a number from one side, then you gotta subtract it from the other.

get the drift....

----

Suggestion: Do you studying at Barnes & Nobles or other bookstore. They have tables and are open late (until 11PM here in USA). When stuck - go to math section and use their books. If you find one you like - then buy it.

Bonus: They have bathrooms and a cafe at most stores -- and you can eat while you study as opposed to the library.

===========

Hope this helps.

John Coxey
(jpcoxey@aol.com)
4. All:

- Did not know there were numbers involved. Just thought we were manipulating the equation.

So here goes:

z=-1.5
a=75
c=10
What is b?

From Step #7 above:

B = A - CZ

B = (75) - (10)( -1.5)

-- Rember the order of operations: Parenthesis, then Multiplation and Division, then Addition and Subtraction.

So: Mulitply first:

B = (75) - ( - 15) <-- HINT: PUT PARENS AROUND NEGATIVE NUMBERS.

B = 75 + 15
B = 90

John Coxey
5. Huh?

Sorry,John,but despite your heroic efforts,I'm still stupid!
6. I am so impressed, I can't get my chin off my desk!! You do rock, John!

When I have "played" w/ math, the thing I keep coming back to is: put your mind in neutral and follow the directions--find an example that matches the problem in the text, copy it, then try it again, using your problem.

To me, math is more like a rheostat than an on/off switch--after a while, you're not sure HOW you 'got it', but it seems to be working, so don't argue, just keep going.

I do agree that you need to understand this stuff--this is your foundation, further down the line, teachers will be expecting to build on this foundation, if its not solid....you're goin' down!!
7. ayemmeff:

- Make a list of math rules - and memorize them to the point that you can do total recall from memory. Best place to start is with the inside front and back covers of your text book. Usually, they will have top-level rules that you need to know.

- Better yet. Get one of those lamiated study guides. They are one or two pages and are crammed full of info. Memorize it. Better yet, make your own as you go through the course. Again, memorize it.

---------

If you have to. Lock yourself in the car. Take a pillow and recline the seat back. If that's what it takes. You gotta put the time into it.

Yeah - that's what it took for me to get though Calculus. Just studied in car out in parking lot.

Gotta run,

John Coxey
8. John,you are a certified Darling! Did you take the same "Patience with Idiots" Class as Obnurseheather,I wonder??
9. I'd ask John to marry me, but I don't think the current husband would agree with the decision. Still, I'm smitten. :kiss

My HP 48GX graphing calculator is getting all hot and bothered...way to go, and welcome to the boards, John.

10. Hey all:

- Thanks for the kinds replies.

- Got a question --- how difficult is Anatomy I & II. What were
the courses like? What did you like or dislike about them?

- I am totally new to the nursing field - so any help would be
appreciated.

Thanks again.

John Coxey
(jpcoxey@aol.com)
11. John, A&P I and II. I wouldn't recommend taking them in the summer, a lot of information in a short time.

They are two of the most important classes (pre-req's) you'll use alot when you get into the nursing courses.