Solving Rational Equations

zee-f · 2011-09-19 09:01:48

heres the options for it

bobbym · 2011-09-19 09:02:55

When I get stuck on any problem I try some numbers to get a feel for what I am trying to understand.

Supposing and bear with me, you used 50 quarts of A and 50 quarts of B. What would your mixture be?

zee-f · 2011-09-19 09:12:11

i would go with d

bobbym · 2011-09-19 09:16:31

Hi zee-f;

If D is A = 30 and B = 60 then I like it also. But that is not what I asked you to do. Please look at #52 again.

zee-f · 2011-09-19 09:19:06

so i would subtract 50% answering what u told me to do

zee-f · 2011-09-19 09:24:06

i was wondering if this equation can do in this

(present A)*(amount A)+(presentB)*(amount B)= (final%)*(final amount)

zee-f · 2011-09-19 09:25:34

i choose D for all of them

18. Solve the problem in question 17.

A 40 quarts of Type A cream and 50 quarts of Type B cream are needed.
B 60 quarts of Type A cream and 30 quarts of Type B cream are needed.
C 24 quarts of Type A cream and 66 quarts of Type B cream are needed.
D 30 quarts of Type A cream and 60 quarts of Type B cream are needed.
E 18 quarts of Type A cream and 72 quarts of Type B cream are needed.
F 35 quarts of Type A cream and 55 quarts of Type B cream are needed.

19. A certain chain saw requires a fuel mixture of 5.5% oil and the remainder gasoline. How many liters of 2.5% mixture and how many of 9% mixture must be combined to produce 40.0 liters of 5.5% mixture?

A 12 4/23 liters of 2.5% and 28 19/23 liters of 9%
B 28 19/23 liters of 2.5% and 12 4/23 liters of 9%
C 21 liters of 2.5% and 18 liters of 9%
D 18 6/13 liters of 2.5% and 21 7/13 liters of 9%
E 21 7/13 liters of 2.5% and 18 6/13 liters of 9%
F 18 7/13 liters of 2.5% and 21 6/13 liters of 9%

20. Mary can row at the rate of 4 miles per hour in still water. Rowing downstream in a river, she can travel 3 times as far in 1 hour as she can rowing upstream. What is the rate of flow in the river?

A 1 miles per hour
B 2.5 miles per hour
C 4 miles per hour
D 2 miles per hour
E 3.5 miles per hour
F 3 miles per hour

Last edited by zee-f (2011-09-19 09:27:46)

bobbym · 2011-09-19 09:29:00

Hold on you are jumping ahead. Let's do one thing at a time.

Call x the amount of A needed.
Call y the amount of b needed.

50 quarts of A means 50 (.18)
50 quarts of B means 50 (.24)

50 (.18) = 9 quarts of fat
50 (.24) = 12 quarts of fat

Understand up to here?

zee-f · 2011-09-19 09:31:52

why did u say 50 quarts

bobbym · 2011-09-19 09:41:00

Because it is easy to calculate! I know it violates one of the conditions of the question but we are just experimenting.

zee-f · 2011-09-19 09:55:30

its past 12 here am ganna get some good sleep and work on it tomorrow i did way to many math problems for today thank you guys for alllll your help

bobbym · 2011-09-19 09:59:22

Hi zee-f;

Get some rest, you did well. I am happy with your progress. I will provide the complete working of the problem for you by tomorrow.

zee-f · 2011-09-20 03:06:20

hey bobbym see the "Work" Word Problems were fun and i get them but the "Mixture" Word Problems are really hard and i dont know how to even start on one

reconsideryouranswer · 2011-09-20 03:37:14

bob bundy wrote:

Bob

Strong advice for everyone:

Do not mix the "times sign" with the algebraic operations/expressions.

Keep the "times sign" within arithmetic.

Keep the "times sign" out of algebra.

Instead, use a multiplication dot or grouping symbols for the multiplication.

------------------------------------------------------------------------------------------

zee-f,

when solving any equation where the variable is in a denominator,
make sure you omit any (candidate) solutions that would cause
one (or more) denominators to equal zero, because those would
make the value of those algebraic fractions undefined.

Last edited by reconsideryouranswer (2011-09-20 03:44:07)

bobbym · 2011-09-20 06:41:57

Hi zee-f;

hey bobbym see the "Work" Word Problems were fun and i get them but the "Mixture" Word Problems are really hard and i dont know how to even start on one

They are a little bit harder but with practice you can get them.
Did you see the solution in post #62? It only looks tricky but
it is not. After a while you will do them easily.

zee-f · 2011-09-20 09:12:58

hey bobbym
am trying my best to try to understand this lesson

am getting 22x+22y=18y+24y is that a right step?

bobbym · 2011-09-20 09:23:23

Type A cream is 18% butterfat and type B cream is 24% butterfat. Set up a table to help you determine how many quarts of each type of cream must be used to create a 90 quart mixture that is 22% butterfat.

Call x the amount of A needed in quarts.

Call y the amount of B needed in quarts.

The first thing you can see from the problem is x + y = 90.

zee-f · 2011-09-20 09:37:31

so

x(9/50)+y(6/25)=11/50?

or
x(9/50)+y(6/25)=90

bobbym · 2011-09-20 09:51:23

Hold on, one step at a time. You have two variables so you need to equations
to solve for them.

So scaling the coefficients we get:

Which verifies your solution.

Can you now solve that set of simultaneous equations?

zee-f · 2011-09-20 10:27:54

ok so i cross multiply first

bobbym · 2011-09-20 10:32:58

First simplify the first equation by using algebra.

Subtract 22 y from both sides.

Subtract 18x from both sides:

Divide by 2:

Now you have the simpler set.

zee-f · 2011-09-20 10:45:18

2x + x = 90

3x = 90

x = 30

bobbym · 2011-09-20 10:47:13

Correct! What does x stand for?

zee-f · 2011-09-20 10:52:37

amount of A needed in quarts

bobbym · 2011-09-20 10:53:34

Correct. So if you mix 30 quarts of A with 60 quarts of B you will have a 22% solution of butterfat.

Math Is Fun Forum

#51 2011-09-19 09:01:48

Re: Solving Rational Equations

#52 2011-09-19 09:02:55

Re: Solving Rational Equations

#53 2011-09-19 09:12:11

Re: Solving Rational Equations

#54 2011-09-19 09:16:31

Re: Solving Rational Equations

#55 2011-09-19 09:19:06

Re: Solving Rational Equations

#56 2011-09-19 09:24:06

Re: Solving Rational Equations

#57 2011-09-19 09:25:34

Re: Solving Rational Equations

#58 2011-09-19 09:29:00

Re: Solving Rational Equations

#59 2011-09-19 09:31:52

Re: Solving Rational Equations

#60 2011-09-19 09:41:00

Re: Solving Rational Equations

#61 2011-09-19 09:55:30

Re: Solving Rational Equations

#62 2011-09-19 09:59:22

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#63 2011-09-20 03:06:20

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#64 2011-09-20 03:37:14

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#65 2011-09-20 06:41:57

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#66 2011-09-20 09:12:58

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#67 2011-09-20 09:23:23

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#68 2011-09-20 09:37:31

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#69 2011-09-20 09:51:23

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#70 2011-09-20 10:27:54

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#71 2011-09-20 10:32:58

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#72 2011-09-20 10:45:18

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#73 2011-09-20 10:47:13

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#74 2011-09-20 10:52:37

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#75 2011-09-20 10:53:34

Re: Solving Rational Equations

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