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mananth answered: 12270 problems
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Rate-of-work-word-problems/324901: Sally can paint a room in 6 hours while it takes Steve 8 hours to paint the same room. How long would it take them if they worked together?
1 solutions
Answer 232620 by mananth(12270)   on 2010-07-23 04:22:35 (Show Source):
You can put this solution on YOUR website!LET PAINTING THE ROOM BE 1JOB
Sally can do the job in 6 hours
she does 1/6 of the job in 1 hour
Steve takes 8 hours to do the job.
he does 1/8 of the job in in 1 hour.
together they do 1/6 + 1/8 of the job in 1 hour
1/6 + 1/8 = 4+3/24 = 7/24 of the job in 1 hour
For doing 1 job together they will take 24/7 hours
= 3.42 hours
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Rectangles/324864: the perimeter of rectangle is 120ft. the length of rectangle is twice the width. find the length and the width of the rectangle.
the perimeter of traingle is 110 cm. one side is twice the second side. the third side is 30 cm more the than second side. find the length of each side.
1 solutions
Answer 232619 by mananth(12270) on 2010-07-23 01:17:41 (Show Source):
You can put this solution on YOUR website!let width be x
length of rectangle = 2x
,,
Perimeter of rectangle = 2L+2W
2x+4x=120
6x=120
x=20 feet which is the width
..
length = 2x = 2*20 =40 feet
..
let second side be x
first side will be 2x
Third side = x+30
Perimeter = 110
..
Perimeter = aum of all sides
x+2x+x+30= 110
4x+30 =110
4x=80
x=20 cm - second side
first side = 2x = 40cm
third side = x+30 = 20+30=50 cm
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Trigonometry-basics/324883: A consultant charges $45 for each hour she works on a
consultation, plus a flat $30 consulting fee. How many
hours of work are included in a $210 bill for a
consultation?
1 solutions
Answer 232613 by mananth(12270) on 2010-07-22 23:35:08 (Show Source):
You can put this solution on YOUR website!$45 for each hour
a flat $30 consulting fee.
$210 bill
..
let the number of hours she worked be x
$45 /hour
charges for hours= 45x
..
45x + 30 = 210
add -30 to both sides
45x +30-30=210-30
45x=180
x=180/45
x= 4 the number of hours she works.
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Problems-with-consecutive-odd-even-integers/324893: 11:34:34 PM ] Guest : What are the three consecutive even integers such that ten time the first integer is equal to six times the sum of the second and third?
[ 11:38:12 PM ] Guest : Hi I have worked on this for hours. College, Susan Intermediate Algebra
[ 11:41:05 PM ] : This was my last attempt before asking for help 10x = 6(3x+6)
[ 11:42:48 PM ] : 10x = 12x+36 take 12x from both sides
[ 11:44:00 PM ] : you get -2x=36 divide both sides by -2
[ 11:44:46 PM ] : x = -18 is this one of the integers?
[ 11:47:26 PM ] : help please!!
1 solutions
Answer 232612 by mananth(12270) on 2010-07-22 23:14:43 (Show Source):
You can put this solution on YOUR website!let the integers be x, x+2, x+4
..
10 times the first integer = 10x..............1
..
sum of second and third
= x+2 +x+4
=2x+6
6 times the sum
6(2x+6)
=12x+36................2
equation 1 = equation 2
10x=12x +36
add -12x to both sides
10x-12x= 12x-12x+36
-2x=36
x= 36/-2
x=-18 . first integer
x+2 = -18+2=-16 second integer
..
x+4 = -18+4
=-14 third integer
...
Check 10x= 6(x+x+6)
10*-18=6(-18-18+6)
-180=-180
the integers are -18,-16,-14
you are right
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Linear-equations/324861: 2y + 3x = 12
-4y + 5x = -2
How do I solve the above liner equations using the elimination method? Can someone kindly explain it to me thanks
1 solutions
Answer 232592 by mananth(12270) on 2010-07-22 21:38:50 (Show Source):
You can put this solution on YOUR website!2y + 3x = 12............1
-4y + 5x = -2...........2
to eliminate a variable the co-efficients of either x or y have to be same in both the equations.
If we multiply equation 1 by 2 then the co-fficient of y will be same.
multiply and add the equations
2(2y+3x)-4y+5x = 24 -2
4y+6x-4y+5x=22
11x=10
x=22/11
x=2
plug the value of x in equation 1
2y+3*2=12
2y+6=12
2y=12-6
y2y=6
y=3
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test/324600: hi i would like your help to help me with this question. Thanks
quesion: 1/r=1/r1 + 1/r2
Express r1 in terms of r and r2
1 solutions
Answer 232353 by mananth(12270) on 2010-07-22 03:42:58 (Show Source):
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Rate-of-work-word-problems/324602: a tank which has an inlet valve through which it get filled in 5 hours and outlet valve through which it becomes empty in 10 hours. when both are open how long will it take to fill the tank?
1 solutions
Answer 232352 by mananth(12270) on 2010-07-22 03:38:41 (Show Source):
You can put this solution on YOUR website!Filling or draining the complete tank is considered as 1 job
filling in 5 hours
so 1/5 of the job in 1 hour.
..
draining in 10 hours
1/10 of the job in 1 hour
..
effective filling when both are open =
1/5 - 1/10 hours
10-5/50= 5/50= 1/10
when both are open
1/10 of the job is done in 1 hour
so it will take 10 hours to fill the tank
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Trigonometry-basics/324594: Please explain how to show work for this problem and the answer:
Two ships leave a port at the same time. One travels at 20 miles per hour in a direction N 32 degrees E, and the other travels at 28 miles per hour in a direction S 42 degrees E. How far apart are the two ships after 2 hours?
1 solutions
Answer 232350 by mananth(12270) on 2010-07-22 03:19:59 (Show Source):
You can put this solution on YOUR website!Two ships leave a port at the same time. One travels at 20 miles per hour in a direction N 32 degrees E, and the other travels at 28 miles per hour in a direction S 42 degrees E. How far apart are the two ships after 2 hours?
..
One travels at 20 mph for 2 hours . = 40 miles N32 deg E
Second travels 28mph for 2 hours . = 56 miles S42 deg E
42 +32 = 74 deg angular distance
..
We have to use the law of cosines to find the the distance.
distance^2= 40^2+60^2-2(40)(60)cos 74
=1600+3600*4800*cos74
=distance ^2=375.75
distance = sqrt375.75
=66.14 miles apart.
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Travel_Word_Problems/324595: Rene is going to the lake to visit some friends. If the lake is 60 miles away, and Rene is driving at 40 miles per hour the entire time, how long will it take her to get to the lake?
1 solutions
Answer 232349 by mananth(12270) on 2010-07-22 02:24:45 (Show Source):
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Square-cubic-other-roots/324596: Question: square root 3 plus square root 27 equals
v3 + v27 = 4v3 (note: the "v" really stands for "square root" in the equation)
I have the answer- but do not know how solve step by step. Can you help me?
Thank you, Drew
1 solutions
Answer 232348 by mananth(12270) on 2010-07-22 02:22:06 (Show Source):
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Angles/324597: the supplement of an angle is 15degrees more than four times its compliment. find the angles its compliment and its supplement?
1 solutions
Answer 232347 by mananth(12270) on 2010-07-22 02:12:51 (Show Source):
You can put this solution on YOUR website!let the angle be x
the complement will be 90-x
..
the supplement will be 180-x
..
four times the complement = 4(90-x)
Add 15 to it
4(90-x)+15 = 180-x
360-4x +15=180-x
-4x+x=-360-15+180
-3x=-195
x=-195/-3
x= 65 deg
The complement = 90-65=25 deg
the supplement of the angle = 180 -x=180-65=115 deg
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Mixture_Word_Problems/324552: A chemical manufacturer wishes to fill an order of 800 gallons of 25% acid solution. Solution of 25% and 35%are in stock. How many gallons of each solution must be mixed to fill the order?
1 solutions
Answer 232278 by mananth(12270) on 2010-07-21 21:41:12 (Show Source):
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Age_Word_Problems/324354: six years ago i was three times as old as my brother and now i am twice as old; find our present ages?
1 solutions
Answer 232149 by mananth(12270) on 2010-07-21 09:33:48 (Show Source):
You can put this solution on YOUR website!let brother's age = x
my age = 2x
..
6 years ago our ages were:
brother - x-6
myself 2x-6
..
I was 3 time his age then
2x-6 = 3(x-6)
2x-6 = 3x-18
3x-2x=18-6
x=12 years brother's age
My age now = 24 years.
..
Your feedback is very valuable for improving the solution.
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Age_Word_Problems/324356: the sum of the ages of father and son is 55 years.after 16 years the father will be twice as old as his son, what are their present ages?
1 solutions
Answer 232145 by mananth(12270) on 2010-07-21 09:29:59 (Show Source):
You can put this solution on YOUR website!let the age of son be x
father's age = 55-x
..
after 16 years their ages will be:
son x+16
father 55-x+16= 71-x
..
Father's age = twice son's age
71-x= 2(x+16)
71-x = 2x +32
3x= 71-32
3x=39
x=13 years , son's age
Father's age = 55-x
= 55-13
=42 years
Your feedback is very important for improving the solution
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Geometry_Word_Problems/324352: A farmer owns a square field of side with a pole in one of the corners to which he tied his cow with a rope whose length is about is 10 m . what is the area available for the cow to grace.
A.150 sq.m b.125sq,m c.75sq.m d. not enough data.
1 solutions
Answer 232141 by mananth(12270) on 2010-07-21 09:24:19 (Show Source):
You can put this solution on YOUR website!the rope is 10 m
tied at one end of a pole.
..
It can move in the field maximum from one side of the square to the other taking a circular path.
..
It can graze only an area of 1/4 of the area of a circle with radius 10m.
..
Area of circle with radius 10 = pi*10^2
Area = 314 sq. m
1/4 of 314 = 78.5 sq. m
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Travel_Word_Problems/324294: if a car takes 20 minutes to travel 15km how fast is the car going ?
1 solutions
Answer 232103 by mananth(12270) on 2010-07-21 04:05:16 (Show Source):
You can put this solution on YOUR website!if a car takes 20 minutes to travel 15km how fast is the car going ?
..
since distance is in km
time has to be changed to hours
20 minutes = 20/60 = 1/3 hours
..
speed = distance / time
speed = 15 / (1/3)
speed = 15*3
= 45 km / hour
..
Your feedback is important to improve the solution
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Equations/324297: Hi I would really like help to solve this question.
Rewrite the following in a shortened form:
(x-3)x(x+3)=?
Please show me how to do this and explain it.
Thanks.
1 solutions
Answer 232102 by mananth(12270) on 2010-07-21 04:01:07 (Show Source):
You can put this solution on YOUR website!(x-3)x(x+3)
this means x*(x-3)*(x+3)
First solve the brackets
multiply each term in bracket 1 to each term in bracket 2
x{x*(x+3)-3(x+3)}
x{x^2+3x-3x-9} +3x & -3x cancel off
x{x^2-9)
x^3-9x
..
Your feedback is valuable for improving the solution
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Linear-systems/324283: At maximum speed an airplane travels 2,460 miles against the wind in 6 hours. Flying with the wind the plane can travel the same distance in 5 hours. What is the speed of the plane with no wind?
1 solutions
Answer 232092 by mananth(12270) on 2010-07-21 00:02:00 (Show Source):
You can put this solution on YOUR website!let speed of wind be y mph
let speed of plane in still air be x
..
Against wind the speed = x-y
distance traveled = 2460
2460/x-y= 6
6x-6y= 2460
x-y=410...........1
..
with wind speed = x+y
distance is same 2460
2460/x+y=5
5x+5y=2460
x+y=492............2
..
Add equation 1 & 2
x-y+x+y=410+492
2x=902
x= 451 mph speed of plane in still air.
..
Plug the value of x in equation 1
451-y=410
y=451-410
y=40 mph the speed of wind
.
Your feed back about the solution is very important in improvement.
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Miscellaneous_Word_Problems/324274: Suppose Wal-Mart stock is selling at $59 a share,and Mattel stock is selling at 28 a share. Amy has a maximum of $6000 to invest. she wishes to purchase four times as many shares of Wal-Mart as Mattel. Only whole shares of stock can be purchased.
A) how many shares of each will she purchase?
B) how much money will be left over.
I have tried figuring it out but can not.
1 solutions
Answer 232091 by mananth(12270) on 2010-07-20 23:51:27 (Show Source):
You can put this solution on YOUR website!Wal-Mart stock $59 a share,
Mattel stock 28 a share.
Amy has a maximum of $6000 to invest.
she wishes to purchase four times as many shares of Wal-Mart as Mattel
..
let Mattel shares she buys be x
Mattel stock 28 a share.
Wal-Mart will be 4x
Wal-Mart stock $59 a share,
Amount invested = $ 6000
..
28x+59*4x<6000
28x+236x<6000
264x< 6000
x< 6000/264
x<22.4
So she buys 22 shares of Mattel
Wal-Mart will be 4x = 4*22=88 shares
88*59 +22*28= 5808
6000-5808=192
She has $192 balance after buying 22 shares of Mattel & 88 shares of Wal-Mart.
CHECK
IN the balance $192 she cannot buy 1 share of Mattel & 4 shares of Wal-Mart which will cost 59*4 +28*1=$264
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Linear-equations/324254: How are addition and multiplication use to solve a linear equation? Demonstrate by solving "(1/5) x - (2/3) = 6x(2/5)"
1 solutions
Answer 232090 by mananth(12270) on 2010-07-20 23:17:46 (Show Source):
You can put this solution on YOUR website!(1/5) x - (2/3) = 6x(2/5)
..
Add +2/3 to both sides
(1/5) x - (2/3)+2/3 = 6x(2/5)+2/3
..
(1/5) x = 6x(2/5)+(2/3)
..
add - 6x(2/5) on both sides
(1/5)x -6x(2/5) =6x(2/5) -6x(2/5)+(2/3)
..
(1/5)x -6x(2/5) = 2/3
LCM = 5 on left side
x-12x /5 =2/3
-11x/5 =2/5
multiply by 5
-11x/5 *5 = 2/5 *5
-11x=2
divide by -11
-5x/-11= 2/-11
x= - 2/11
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Systems-of-equations/323997: Solve the system of equations.
2x-7y=3
-33=-7x+2y
1 solutions
Answer 231884 by mananth(12270) on 2010-07-20 11:06:54 (Show Source):
You can put this solution on YOUR website!2x-7y=3
-33=-7x+2y
..
2x-7y=3............1
7x-2y=33...........2
..
multiply equation 1 by 7 and equation 2 by 2 to eliminate x
14x-49y=21
14x-4y=66
subtract
14x-49y-14x+4y=21-66
-45y=-45
y=1
plug the value of y in equation 1
2x-7=3
2x=10
x=5
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Miscellaneous_Word_Problems/323965: The cost in dollars of manufacturing x refrigerators is 9000 + 400x. the amount received when selling these x refrigerators is 500x dollars. what is the least number of refrigerators that must be manufactured and sold so that the amount received is at least equal to the manufacturing cost ?
A 10 B 18 C 45 D 90 E 100
1 solutions
Answer 231881 by mananth(12270) on 2010-07-20 10:55:17 (Show Source):
You can put this solution on YOUR website!9000+400x is the cost of x refrigerators
sales value = 500x
They have to be same to break even
..
9000+400x =500x
9000=500x-400x
100x=9000
x= 90 refrigerators
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Percentage-and-ratio-word-problems/323971: In a certain shop , notebooks that normally sell for 59 cents each are on sale at 2 for 99 cents . how much can be saved by purchasing 10 of these notebooks at the sale price ?
A $0.85 B $0.95 C $1.10 D $1.15 E $2.00
1 solutions
Answer 231879 by mananth(12270) on 2010-07-20 10:43:50 (Show Source):
You can put this solution on YOUR website!normal price = 59 cents
..
sale price = 2 for 99
so 1 costs 99/2 = 49.5 cents
the difference = 59-49.5 = 9.5 cents / book
so for 10 books the difference will be 95 cents
OR $0.95
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Age_Word_Problems/323957: Mary is presently twice as old as Maggy. Ten years ago, Maggy's age was one-third of Mary's then. Ten years from now, Maggy's age will be three-fifths of Mary's age then. How old is each?
1 solutions
Answer 231875 by mananth(12270) on 2010-07-20 10:33:53 (Show Source):
You can put this solution on YOUR website!Let Maggy's age = x
Mary's age = 2x
..
ten years later their ages will be
Maggie= x+10
Mary = 2x+10
..
x+10 = 3/5 (2x+10)
5(x+10)=3(2x+10)
5x+50=6x+30
6x-5x=50-30
x=20 years Maggie's age
Mary's age = 2x = 40 years
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