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percentage/388806: Please help me solve this problem: a commission of $168 on $560 is a commission Of what per cent?
1 solutions

Answer 275216 by josmiceli(9686) About Me  on 2010-12-26 03:22:56 (Show Source):
You can put this solution on YOUR website!
Per cent means "per one hundred".
In place of "what per cent" I can
put in x%2F100
Now I just read the sentence
$168 is x%2F100 x $560
or
168+=+%28x%2F100%29%2A560
Multiply both sides by 100
16800+=+560x
x+=+30
a commission of $168 on $560
is a commission Of 30 per cent


Money_Word_Problems/388776: If $2500 is invested at a rate of 11% compounded continuously, find the balance in the account after 4 years. Use the formula A=Pe^rt.
a.3795.18 b.3881.77 c.4333.13 d.18472.64
*the answers I'm getting do not match the answers above. please help.
1 solutions

Answer 275181 by josmiceli(9686) About Me  on 2010-12-25 17:37:48 (Show Source):
You can put this solution on YOUR website!
A+=+P%2Ae%5E%28r%2At%29
given:
P=+2500
r+=+.11
t+=+4
---------
A+=+2500%2Ae%5E%28.11%2A4%29
A+=+2500%2Ae%5E.44
A+=+2500%2A1.5527
A+=+3881.768
This is close to (b). You are doing something wrong with
your calculator, I think.


Radicals/388732: Can you please help me i am doing radicals and square roots. i am having so much problems.
Here are the problems:
1.)square root of 128y^4 fraction bar 64^2
2.)square root of 64x^2, 21y^3, 72z^2
Thank you very much
1 solutions

Answer 275102 by josmiceli(9686) About Me  on 2010-12-24 15:11:06 (Show Source):
You can put this solution on YOUR website!
1)
Is the problem sqrt%28128%2Ay%5E4%2F64%5E2%29 ?
If so, think of it in a way that makes sense to you.
You should know both of these basic rules:
%28sqrt%28x%29%29%5E2+=+x
and
sqrt%28x%5E2%29+=+x
sqrt%28x%5E2%29+=+-x
Of course, x can be any positive number
Rewrite your problem to simplify it
sqrt%282%2A64%2Ay%5E4%2F64%5E2%29
Right away I see that 64%2F64%5E2+=+1%2F64, so now I have
sqrt%282%2Ay%5E4%2F64%29
This is the same as
sqrt%281%2F64%29%2Asqrt%282%2Ay%5E4%29
%281%2F8%29%2Asqrt%282%2Ay%5E2%2Ay%5E2%29
%281%2F8%29%2Asqrt%282%29%2Asqrt%28y%5E2%29%2Asqrt%28y%5E2%29
%281%2F8%29%2Asqrt%282%29%2Ay%2Ay
%281%2F8%29%2Asqrt%282%29%2Ay%5E2
This answer can actually be plus or minus. I don't know if you've
covered this yet
I'll do 1 more:
sqrt%2821y%5E3%29
There are no perfect squares contained in 21, since
the only factors are 3 and 7
sqrt%2821%29%2Asqrt%28y%5E2%29%2A+sqrt%28y%29
From the rules:
sqrt%2821%29%2Ay%2Asqrt%28y%29
This answer is NOT plus or minus because of the odd exponent in y%5E3


Miscellaneous_Word_Problems/388733: A container with a square base, vertical sides,
and open top is to be made from 1000 ft2 of material.
(a) Write an equation for the volume of the con-
tainer as a function of the length of a side of
the base.
(b) Write an equation for the volume of the con-
tainer as a function of the length of the ver-
tical side
I can do part (a) but I am stuck on (b), Help would be greatly appreciated. Thanks
1 solutions

Answer 275099 by josmiceli(9686) About Me  on 2010-12-24 14:31:53 (Show Source):
You can put this solution on YOUR website!
(a)
The square base can be any size, so I'll call
the sides of the base x.
I want the 1000 ft2 of material to be a
square also, so the sides of the container will
all be the same height .
that means each side of the material will be
10%2Asqrt%2810%29 ft2
I'll place the x%5E2 ft2 base exactly in the center.
That means the 4 sides will measure x by %2810%2Asqrt%2810%29+-+x%29%2F2
Let V = volume
V+=+x%5E2%2A%2810%2Asqrt%2810%29+-+x%29%2F2
V+=+5%2Asqrt%2810%29%2Ax%5E2+-+x%5E3%2F2
Is this what you got?
(b)
I'll call the length of the vertical side y
y+=+%2810%2Asqrt%2810%29+-+x%29%2F2
Ok, now I can say that
V+=+x%5E2%2Ay
Now I just have to find x in terms of y,
so I go back to y+=+%2810%2Asqrt%2810%29+-+x%29%2F2
2y+=++10%2Asqrt%2810%29+-+x
x+=+10%2Asqrt%2810%29+-+2y
Now I can say
V+=+%2810%2Asqrt%2810%29+-+2y%29%5E2+%2Ay
V+=+%281000+-+40%2Asqrt%2810%29%2Ay+%2B+4y%5E2%29%2Ay
V+=+4y%5E3+-+40%2Asqrt%2810%29%2Ay%5E2+%2B+1000y
Check answer:
Suppose y+=+1
That would mean x+=+10%2Asqrt%2810%29+-+2
V+=+1%2A%281000+-+40%2Asqrt%2810%29%29+%2B+4
V+=+1004+-+40%2Asqrt%2810%29
The equation gives me:
V+=+4y%5E3+-+40%2Asqrt%2810%29%2Ay%5E2+%2B+1000y
V+=+4+-+40%2Asqrt%2810%29+%2B+1000
same answer


Miscellaneous_Word_Problems/388274: 3.mr. kumar lives in the eastern part of the singapore. he visits his aged parents who lives 36 km away, evry weekends. he finds that if he increases the average speed of his vehicle by 12 km/h.he could save 9 min of his travelling time. find the speed at which he travels before the increase in speed
1 solutions

Answer 274602 by josmiceli(9686) About Me  on 2010-12-21 15:33:36 (Show Source):
You can put this solution on YOUR website!
Let t = his time before he increases his speed.
Let r = his rate before he increases his speed
given:
(1) 36+=+r%2At
(2) 36+=+%28r+%2B+12%29%2A%28t+-+9%2F60%29
----------------------
(2) 36+=+r%2At+%2B+12t+-+%283%2F20%29%2Ar+-+9%2F5
Substituting from (1):
36+=+36+%2B+12%2A%2836%2Fr%29+-+%283%2F20%29%2Ar+-+9%2F5
Multiply both sides by 20r
0+=+24%2A360+-+3r%5E2+-+36r
3r%5E2+%2B+36r+-+8640+=+0+
r%5E2+%2B+12r+-+2880+=+0
Use quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+1
b+=+12
c+=+-2880
x+=+%28-12+%2B-+sqrt%28+12%5E2-4%2A1%2A%28-2880%29+%29%29%2F%282%2Aa%29+
x+=+%28-12+%2B-+sqrt%28+144+%2B+11520+%29%29%2F2+
x+=+%28-12+%2B-+sqrt%28+11664+%29%29%2F2+
r+=+%28-12+%2B+108%29%2F2
r+=+96%2F2
r+=+48
the other root is ignored since it is negative
His speed before the increase is 48 km/hr
Check answer:
(1) 36+=+r%2At
t+=+36%2F48
t+=+3%2F4
(2) 36+=+%28r+%2B+12%29%2A%28t+-+9%2F60%29
36+=+%2848+%2B+12%29%2A%283%2F4+-+9%2F60%29
36+=+60%2A%283%2A15+-+9%29%2F60
36+=+45+-+9
36+=+36
OK


Inequalities/387944: Adult tickets for a play cost $14 and child tickets cost $3.
If there were 26 people at a performance and the theater collected $199
from ticket sales, how many adults and how many children attended the play?
1 solutions

Answer 274239 by josmiceli(9686) About Me  on 2010-12-19 21:02:44 (Show Source):
You can put this solution on YOUR website!
Let a = number of adult tickets sold
Let b = number of child tickets sold
given:
(1) a+%2B+b+=+26
(2) 14a+%2B+3b+=+199
-------------------
Multiply both sides of (1) by 3
and subtract (1) from (2)
(2) 14a+%2B+3b+=+199
(1) -3a+-+3b+=+-78
11a+=+121
a+=+11
and, since
(1) a+%2B+b+=+26
b+=+26+-+11
b+=+15
11 adults and 15 children attended


Equations/387807: write in standard form an equation of the line that passes trough the given point and has the given slope.Use integer coefficient. (6,-1),m=0
1 solutions

Answer 274158 by josmiceli(9686) About Me  on 2010-12-19 13:16:28 (Show Source):
You can put this solution on YOUR website!
y+=+mx+%2B+b
given:
m+=+0
y+=+0%2Ax+%2B+b
y+=+b
The line passes through (6,-1), so
y+=+-1
y+=+-1 answer
Note that y is always the same no matter what x isThe plot is:
+graph%28+400%2C+400%2C+-5%2C+5%2C+-4%2C+1%2C+-1%29+


Miscellaneous_Word_Problems/387814: A sale at Carney's Electronics offers a specific model of sony radio at 20% off the regular price. If the sale price of the radio is $45, what is the regular price?
1 solutions

Answer 274152 by josmiceli(9686) About Me  on 2010-12-19 13:05:23 (Show Source):
You can put this solution on YOUR website!
Let p = regular price
given:
p+-+.2p+=+45
.8p+=+45
p+=+56.25


Polynomials-and-rational-expressions/387765: I can't seem to get this right, please help?
Use polynomial long division to divide
-4x3 + 24x2 – 24x + 4
by
x2 – 5x + 1
1 solutions

Answer 274147 by josmiceli(9686) About Me  on 2010-12-19 12:31:38 (Show Source):
You can put this solution on YOUR website!
My 1st term would be -4x, since
-4x%2A%28x%5E2+-+5x+%2B+1%29+=+-4x%5E3+%2B+20x%5E2+-+4x
and
-4x%5E3+%2B+24x%5E2+-+24x+-+%28-4x%5E3+%2B+20x%5E2+-+4x%29+=+4x%5E2+-+20x
And my next term will be 4, since
4%2A%28x%5E2+-+5x+%2B+1%29+=+4x%5E2+-+20x+%2B+4
and
-4x%5E2+-+20x+%2B+4+-+%284x%5E2+-+20x+%2B+4%29+=+0+
The answer is -4x+%2B+4 (it checks out)


Money_Word_Problems/387763: A musician is planning to market a CD. The fixed costs are $720 and the variable costs are $6 per CD. The wholesale price of the CD will be $10. For the artist to make a profit, revenues must be greater than costs.
How many CDs, x, must be sold for the musician to break even?
1 solutions

Answer 274139 by josmiceli(9686) About Me  on 2010-12-19 11:26:37 (Show Source):
You can put this solution on YOUR website!
Let C = total cost of making x CDs
Let I = total income from making x CDs
given:
C+=+6x+%2B+720
I+=+10x
The problem is asking "When does the income = cost?"
I+=+C
6x+%2B+720+=+10x
4x+=+720
x+=+180
180 CDs must be sold to break even


Money_Word_Problems/387756: if you deposit $150 in an account that earns simple interest.The annual interest rate is 3.2%. How much interest will you earn in 3 years?
1 solutions

Answer 274138 by josmiceli(9686) About Me  on 2010-12-19 11:18:50 (Show Source):
You can put this solution on YOUR website!
Let x+=+150
Let E = earnings at end of each year
At the end of the 1st year:
E+=+x+%2B+.032x+=+1.032x
At the end of the 2nd year:
E+=+x+%2B+.032x+%2B+.032%2A%28x+%2B+.032x%29
E+=+1.032x+%2B+.032%2A1.032x
E+=+1.032%2A1.032x
E+=+1.032%5E2%2Ax
At the end of the 3rd year:
E+=+1.032%5E2%2Ax+%2B+.032%2A1.032%5E2%2Ax
E+=+1.032%2A1.032%5E2%2Ax
E+=+1.032%5E3%2Ax
Substituting:
1.032%5E3%2A150+=+1.0991%2A150
1.0991%2A150+=+164.866
Interest earned = 164.866+-+150+=+14.87
In 3 years $14.87 interst is earned


absolute-value/387717: joe has a nickles and dime that is worth $2.15. if the number of dimes was doubled and the number of nickles was increased by 28 , the value of the coins would be $6.00. How many nickles and dimes does he has?
1 solutions

Answer 274114 by josmiceli(9686) About Me  on 2010-12-19 03:14:45 (Show Source):
You can put this solution on YOUR website!
Let n = number of nickels
Let d = number of dimes
given:
(1) 5n+%2B+10d+=+215 (in cents)
(2) 10%2A%282d%29+%2B+5%2A%28n+%2B+28%29+=+600
----------------------------------
There are 2 equations and 2 unknowns,
so it's solvable
(2) 20d+%2B+5n+%2B+140+=+600
(2) 5n+%2B+20d+=+460
Now subtract (1) from (2)
(2) 5n+%2B+20d+=+460
(1) -5n+-+10d+=+-215
10d+=+245
d+=+24.5 impossible
In (1), n has to be odd to get 215
In (2), n+%2B+28 ends up being odd again
and that can't give me 600
These numbers are wrong somehow, I think.


Rate-of-work-word-problems/387668: A larger pipe can empty a pool in 6 hrs and a smaller pipe can empty the same pool in 9 hrs. How long will it take both pipes to empty the pool?
1 solutions

Answer 274050 by josmiceli(9686) About Me  on 2010-12-18 19:47:22 (Show Source):
You can put this solution on YOUR website!
Add their rates of emptying to get rate for both
In words:
{1 pool)/(6 hours) + (1 pool)/(9 hours) = (1 pool)/(x hours)
1%2F6+%2B+1%2F9+=+1%2Fx
Multiply both sides by 18x
3x+%2B+2x+=+18
5x+=+18
x+=+3.6
It will take 3.6 hrs or 3 hours and 36 minutes


Travel_Word_Problems/387537: Two trains are traveling in 60 kmph on same trace, towards each other. When the distance between them is 18 km, a fly is going to start, flying between them in 80 kmph speed. Find the traveling path distance of the fly up to when it is going to crush by the 2 trains?
1 solutions

Answer 273973 by josmiceli(9686) About Me  on 2010-12-18 07:24:21 (Show Source):
You can put this solution on YOUR website!
You can think of the situation as 1 of the trains being
stationary and the other moving towards it at the sum of their
speeds, or 60+%2B+60+=+120 km/hr
The fly leaps off the stationary one at 80 km/hr. Now
think of the fly as being stationary, and the other train
coming towards it at the sum of their speeds,
or 120+%2B+80+=+200 km/hr. At that speed, the fly and the train
will meet in 18%2F200+=+.09 hr or 5.4 min
But the trains will meet in 18%2F120+=+.15 hr or 9 min
So, the fly gets to travel for .15+-+.09+=+.06 hr at 120
km/hr and 120%2A.06+=+8.2 km
I get 18+%2B+8.2+=+26.2 km as the distance the fly travels
I am unsure of this. I may only be half right. Check another source.



Linear-equations/387531: Here is my problem. Write the slope-intercept equation for the line with the given slope that contains the given point m=-3/4;(0,5)
1 solutions

Answer 273963 by josmiceli(9686) About Me  on 2010-12-18 01:49:08 (Show Source):
You can put this solution on YOUR website!
The slope-intercept form is
y+=+mx+%2B+b
given:
m+=+-3%2F4
Now you have:
y+=+-%283%2F4%29%2Ax+%2B+b
If the line goes through (0,5), I can say
5+=+-%283%2F4%29%2A0+%2B+b
b+=+5
So, the equation is:
y+=+-%283%2F4%29%2Ax+%2B+5
Here's the plot:
+graph%28+400%2C+400%2C+-2%2C+10%2C+-2%2C+10%2C+-%283%2F4%29%2Ax+%2B+5%29+


Linear-equations/387415: Food-stamp program participation. Participation in the U.S. food-stamp program grew from approximately 17.1 million people in 2000 to approximately 23 million in 2004
Calculate the number of participants in 2001.
b) Predict the number of participants in 2010.
1 solutions

Answer 273962 by josmiceli(9686) About Me  on 2010-12-18 01:41:31 (Show Source):
You can put this solution on YOUR website!
Basically, you need to find the equation
N+=+f%28Y%29, where N is the number of participants
for a given year, and Y is that year
--------------------
You want to plot N on the vertical axis
You want to plot Y on the horizontal axis
Assume the relation between N and Y is linear
given:
17.1+=+f%280%29
23+=+f%284%29
Note that I'm saying 2000+=+0
The slope will be %2823+-+17.1%29%2F%284+-+0%29+=+4.9%2F4
5.9%2F4+=+1.475
So, the equation is:
N+=+1.475Y+%2B+17.1
(a)
N%281%29+=+1.475%2A1+%2B+17.1
N%281%29+=+18.575
There are 18,575,000 participants in 2001
(b)
N%2810%29+=+1.475%2A10+%2B+17.1
N%2810%29+=+14.75+%2B+17.1
N%2810%29+=+31.85
There will be 31,850,000 participants in 2010
Here's the plot:
+graph%28+400%2C+400%2C+-1%2C+12%2C+-4%2C+40%2C+1.475x+%2B+17.1%29+


Average/387522: I have a percent 91% on first test and 87% on second test and 86% on third test what average percent should I receive of the fourth and fifth test to receive a 95%
1 solutions

Answer 273960 by josmiceli(9686) About Me  on 2010-12-18 01:17:58 (Show Source):
You can put this solution on YOUR website!
Let the grades on the 4th and 5th tests = a and b
The problem wants to know what is %28a+%2B+b%29%2F2
given:
%2891+%2B+87+%2B+86+%2B+a+%2B+b%29%2F5+=+95
264+%2B+a+%2B+b+=+5%2A95
a+%2B+b+=+475+-+264
a+%2B+b+=+211
%28a+%2B+b%29%2F2+=+105.5
It looks like you can't average 95% for the 5 tests, because
then you would need to get better than 100% on the 4th and 5th tests


Age_Word_Problems/387528: mary is 24 years old. tina is twice as old as mary 3 years ago. what will be tina's age 5 years from now?
1 solutions

Answer 273959 by josmiceli(9686) About Me  on 2010-12-18 01:06:11 (Show Source):
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Let m = Mary's age now
Let t = Tina's age now
Three years ago, mary was 24+-+3+=+21
Three years ago, Tina was t+-+3
given:
m+=+24
t+-+3+=+2%2A21
-------------------
t+=+42+%2B+3
t+=+45
and
t+%2B+5+=+45+%2B+5
t+%2B+5+=+50
In five years, Tina will be 50 years old


Miscellaneous_Word_Problems/387384: Could someone work this out step by step for me. I do not understand. I am lost.
b^4+13b^2+36=0
Thank you so much.
1 solutions

Answer 273823 by josmiceli(9686) About Me  on 2010-12-17 11:13:43 (Show Source):
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I can say k+=+b%5E2
The equation becomes
k%5E2+%2B+13k+%2B+36+=+0
Using the quadratic formula:
k+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
where
a+=+1
b+=+13
c+=+36
k+=+%28-13+%2B-+sqrt%28+13%5E2-4%2A1%2A36+%29%29%2F%282%2A1%29+
k+=+%28-13+%2B-+sqrt%28+169+-+144+%29%29%2F2+
k+=+%28-13+%2B-+sqrt%28+25+%29%29%2F2+
k+=+%28-13+%2B+5%29%2F2
k+=+-4
and
k+=+%28-13+-+5%29%2F2
k+=+-9
And, since
k+=+b%5E2
-4+=+b%5E2
b+=+2i
and
-9+=+b%5E2
b+=+3i
The roots are imaginary
If I put b+=+3i back into the equation:
%283i%29%5E4+%2B+13%2A%283i%29%5E2+%2B+36+=+0
81+-+117+%2B+36+=+0
117+-+117+=+0
b+=+2i should check also
(note that+i%5E4+=+1)


Angles/387385: Find two complementary angles whose ratio is 4:5.
1 solutions

Answer 273822 by josmiceli(9686) About Me  on 2010-12-17 10:58:30 (Show Source):
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Let the angles be a and 90+-+a
given:
4%2F5+=+a%2F%2890+-+a%29
5a+=+4%2A%2890+-+a%29
5a+=+360+-+4a
9a+=+360
a+=+40
90+-+a+=+50
The angles are 40 degrees and 50 degrees


Graphs/387365: given the graph points of (2,3)(5,5)(8,8) Find the slope of each of the three line segments in the graph. Please show all of your work. Between which two points is the slope the smallest? HELP!!
1 solutions

Answer 273821 by josmiceli(9686) About Me  on 2010-12-17 10:52:25 (Show Source):
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There is a line between the points (2,3) and (5,5)
There is a line between the points (2,3) and (8,8)
There is a line between the points (5,5) and (8,8)
The definition of slope is (change in y)/(change in x)
For the 1st line:
slope = %285-+3%29%2F%285+-+2%29+=+2%2F3
For the 2nd line:
slope = %288+-+3%29%2F%288+-+2%29+=+5%2F6
For the 3rd line:
slope = %288+-+5%29%2F%288+-+5%29+=+1
The smallest slope is 2%2F3, since, using the LCD, the slopes are
4%2F6, 5%2F6, and 6%2F6


Linear-equations/387190: I do not really understand how to solve this.
The question says: "Graph the line passing through (2,4) tbat is perpendicular to the graph of y=-3"
1 solutions

Answer 273681 by josmiceli(9686) About Me  on 2010-12-16 19:59:00 (Show Source):
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A line is perpendicular to another line if their slopes are related this way:
m%5B1%5D+=+-1%2Fm%5B2%5D
where m means slope of the line(s)
It is given that a line has the equation y+=+-3
You usually find m by comparing the given equation
with the general equation y+=+mx+%2B+b, but what
you have is more like y+=+b where b+=+-3,
so m%5B2%5D must be zero.
What is m%5B1%5D?
m%5B1%5D+=+-1%2F0
m%5B1%5D = infinity, or a vertical slope.
So, you have a vertical line that goes through (2,4).
All vertical lines have the form x+=+k
From (2,4), I see that the line is x+=+2


Age_Word_Problems/387104: John is two times older than Mary. Mary is three times younger than Steve. How old is Steve if he is 3 years older than John?
1 solutions

Answer 273631 by josmiceli(9686) About Me  on 2010-12-16 16:15:18 (Show Source):
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given:
(1) j+=+2m
(2) s+=+3m
(3) s+=+j+%2B+3
This is 3 equations and 3 unknowns, so it's solvable
-------------
By substituting (1) into (2):
m+=+j%2F2
(2) s+=+%283%2F2%29%2Aj
j+=+%282%2F3%29%2As
Put this into (3):
s+=+%282%2F3%29%2As+%2B+3
3s+=+2s+%2B+9
s+=+9
Steve is 9 years old
check answer:
j+=+%282%2F3%29%2As
j+=+%282%2F3%29%2A9
j+=+6
and
j+=+2m
m+=+j%2F2
m+=+3
These values check OK


Miscellaneous_Word_Problems/387070: My homework isnt hard a lot of the time, but this problem is REALLY stumping me! Any help?
Last month Cindy Lou ate an unknown number of cans of Who Hash. Her mother ate 7 fewer than 4 times as many cans as Cindy Lou. Her father ate twice as many cans as her mother. Using “h” to represent the number of cans Cindy Lou ate, write an expression to show the total number of cans that Cindy Lou, her mother and father ate. Simplify the expression.
I wrote that
H= Cindy
M=Cindy's Mom
F=Cindy's Father
4h-7= M
2m=F
I understood that two M is F, and two M is Also equal to
8h-14=F
But Im having trouble figuring out how to solve for h in...
Please, help me!
1 solutions

Answer 273625 by josmiceli(9686) About Me  on 2010-12-16 16:05:05 (Show Source):
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You can't solve for h because it's unknown, and the
information given does not make it possible to find.
All they want is basically what you already found
The number of cans of hash is
h+%2B+m+%2B+f
and this equals
h+%2B+4h+-+7+%2B+8h+-+14
This simplifies to
13h+-+21


Average/387082: IT WOULD TAKE BETSEY 4 HOURS TO CLEAN HER ROOM. HER MOM COULD DO IT IN 2 HOURS. USE ALGEBRA TO FIND HOW LONG IT WOULD TAKE THEM WORKING TOGETHER?
1 solutions

Answer 273616 by josmiceli(9686) About Me  on 2010-12-16 15:54:44 (Show Source):
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Think of these problems as adding their
rates of working separately
Let R%5B1%5D = Betsy's rate of working alone
Let R%5B2%5D = Mother's rate of working alone
Let R%5B3%5D = their rate of working together
---------------------------
The rule is:
R%5B1%5D+%2B+R%5B2%5D+=+R%5B3%5D
given:
R%5B1%5D+=+1%2F4
This means 1 room cleaned in 4 hours
R%5B2%5D+=+1%2F2
This means 1 room cleaned in 2 hours
----------------
So far I've got
1%2F4+%2B+1%2F2+=+R%5B3%5D
I can express R%5B3%5D as 1%2Fx, or 1 room
cleaned in x hours
Now I have:
1%2F4+%2B+1%2F2+=+1%2Fx
Multiply both sides by 4x
x+%2B+2x+=+4
3x+=+4
x+=+4%2F3 hours
This is the same as:
%284%2F3%29%2A60+=+80 min, or 1 hour and 20 minutes working together


Miscellaneous_Word_Problems/383394: Bonnie had some stickers. First, Bonnie gave away 1/6 of her stickers. When Bonnie gets 12 more stickers, she has 47 stickers.How many stickers did Bonnie have at the start?
1 solutions

Answer 271459 by josmiceli(9686) About Me  on 2010-12-08 22:04:27 (Show Source):
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Let s = number of stickers to start
given:
s+-+%281%2F6%29%2As+%2B+12+=+47
6s+-+s+%2B+72+=+282
5s+=+210
s+=+42


Proportions/383384: If Jahan can eat 24 hot dogs in 4 minutes, how many hot dogs can he eat in 320 seconds?
1 solutions

Answer 271454 by josmiceli(9686) About Me  on 2010-12-08 21:31:01 (Show Source):
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(4 min) x (60 sec / min) = 240 sec
(24 hotdogs/ 240 sec) = (1 hotdog / 10 sec)
(1 hotdog / 10 sec) x 320 sec = 32 hotdogs


Travel_Word_Problems/383218: Traveling downstream, a boat can go 12 miles in 2 hours. Going upstream it takes only 2/3 the distance in twice the time. What is the rate of the boat in still water, and what is the rate of the current?
1 solutions

Answer 271396 by josmiceli(9686) About Me  on 2010-12-08 17:54:46 (Show Source):
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Let c = rate of current in mi/hr
Let r = rate of boat in still water
r+%2B+c = rate going downstream
r+-+c = rate going upstream
given:
r+%2B+c+=+12%2F2
(1) r+%2B+c+=+6 mi/hr
r+-+c+=+%282%2F3%29%2A12+%2F4
(2) r+-+c+=+2 mi/hr
add (1) and (2)
2r+=+8
r+=+4
and since
r+-+c+=+2
4+-+c+=+2
c+=+2
The rate of the boat in still water is 4 mi/hr
The rate of the current is 2 mi/hr


Surface-area/383225: If the box is 12 inches long, 4 inches wide and 3 inches high, then what is the length of the diagonal?
1 solutions

Answer 271392 by josmiceli(9686) About Me  on 2010-12-08 17:44:19 (Show Source):
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Let d = diagonal
d%5E2+=+12%5E2+%2B+4%5E2+%2B+3%5E2 (in in2)
d%5E2+=+144+%2B+16+%2B+9
d%5E2+=+169
d+=+sqrt%28169%29
d+=+13 in


Geometry_proofs/378225: Well, I am taking geometry and I forgot how to divide fractions. I have 29/3 divided by 3. So I know I change it to 29/3 divided by 3/1, but what comes next?
1 solutions

Answer 268777 by josmiceli(9686) About Me  on 2010-11-30 12:40:09 (Show Source):


Human-and-algebraic-language/378073: i actually have 3 questions.
1. henry wants to join a book of the month club. the first club cost $40 to join and $10 per book. The second club cost $15 per book and has no fee to join. how many books need to be purchased from each club for the clubs to cost the same?
they need to be in an equation.
2. A car's speed before a sudden stop can be estimated by the formula S=30gk, where S=speed of the car in mph, g= drag fact,k=length of skid mark. the drag factor during a recent crash was 0.8. What was the approximate speed of the car if it created skid marks 193 feet long?
3. A group of 3 children and 2 adults pay a total of $120 to take a karate class. A group of 5 children and 1 adult take the same karate class for $95. What is the total cost for 1 child and 1 adult to take the karate class?
1 solutions

Answer 268637 by josmiceli(9686) About Me  on 2010-11-30 05:50:31 (Show Source):
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I can answer (3)
Let c = cost for 1 child
Let a = cost for 1 adult
given:
(1) 3c+%2B+2a+=+120
(2) 5c+%2B+a+=+95
Multiply both sides of (2) by 2
and subtract (1) from (2)
(2) 10c+%2B+2a+=+190
(1) -3c+-+2a+=+-120
7c+=+70
c+=+10
And, from (2),
(2) 5%2A10+%2B+a+=+95
a+=+95+-+50
a+=+45
$10 = cost for 1 child
$45 = cost for 1 adult