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SOLUTION: "SYSTEM OF EQUATIONS" PROBLEM
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 ***
STEP 9: WRITEUP YOUR ANSWER:
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.
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John Coxey
MS-COMPUTER SCIENCE ---> LOOKING TO BECOME RN SOMEDAY I HOPE!!!!
Sorry - could not get equations to line up.
Cut and paste into NotePad. Use CourierNew font so text
will line up. Can't do with default TimesRoman.
Then manually line up the TOP & BOT equations for each
step and things will be much clearer.
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Whenever you get a word problem. Trick is to try to see how
to make it fit into the general equations for the section you
are working on.
If you are doing regular math problems for that section, then
try to make the word problems fit into the regular math problems.
A bear, I know.
I took Calculus 5 times - but ended up with a BS-Applied Mathematics and finally an MS-Computer Science.
Am working in computer industry - but want to pursue career in nursing.
John Coxey
John you boggle my mind!! My daughter is currently in a doctoral program at UC San Deigo. Her area is math. She teaches undergrad as well as completing her own studies--she's only 24! I was chatting with her online just now and was going to ask her the question. I have a ton of respect for people who can explain math...period! Great minds!!
~Sally
ava'smomRN
703 Posts
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 again. can anyone provide a helpful technique. i know it is probaly a very simple question for you all but i can't take it anymore, math is my weakness and i need help
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