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mananth answered: 12270 problems
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11430..11459 , 11460..11489 , 11490..11519 , 11520..11549 , 11550..11579 , 11580..11609 , 11610..11639 , 11640..11669 , 11670..11699 , 11700..11729 , 11730..11759 , 11760..11789 , 11790..11819 , 11820..11849 , 11850..11879 , 11880..11909 , 11910..11939 , 11940..11969 , 11970..11999 , 12000..12029 , 12030..12059 , 12060..12089 , 12090..12119 , 12120..12149 , 12150..12179 , 12180..12209 , 12210..12239 , 12240..12269 , 12270..12299, >>NextRate-of-work-word-problems/358405: A tank can be filled in 2 hours by 2 pipes together.
The larger pipe can fill it in 3 hours less than the smaller.
How long will it take each pipe to fill the tank?
1 solutions
Answer 255783 by mananth(12270)   on 2010-10-19 05:46:44 (Show Source):
You can put this solution on YOUR website!both together take 2 hours
so they do 1/2 the job in1 hour
..
let smaller pipe take x hours
so it will do 1/x of the job in 1 hour
..
second pipe takes x-3 hours
so it does 1/(x-3) of the job in 1 hour
...
1/x + 1/(x-3)=1/2
x-3+x/x(x-3)=1/2
2x-3=1/2* x(x-3)
2(2x-3)=x(x-3)
4x-6=x^2-3x
x^2-3x-4x+6=0
x^2-7x+6=0
x^2-6x-x+6=0
x(x-6)-1(x-6)=0
(x-6)(x-1)=0
x=1 OR 6
x = 1 is not valid
so x=6 hours taken by the pipe alone
second pipe takes 6-3 = 3 hours to fill the tank
...
m.ananth@hotmail.ca
|
Travel_Word_Problems/358406: A car traveled the first 100 kilometers of a trip at one
speed and the last 135 kilometers at an average of
5 kilometers per hour less. If the entire trip took 5 hours,
what was the average speed of the car for the first part
of the trip?
1 solutions
Answer 255781 by mananth(12270) on 2010-10-19 05:36:30 (Show Source):
You can put this solution on YOUR website!A car traveled the first 100 kilometers of a trip at one
speed and the last 135 kilometers at an average of
5 kilometers per hour less. If the entire trip took 5 hours,
what was the average speed of the car for the first part
..
first part 100 km -----------x km/h
second part 135 km---------- x-5 km/h
...
time first part + time second part = 5 hours
100/x + 135/(x-5)= 5
100(x-5)+135x /x(x-5)=5
100(x-5)+135x =x(x-5)*5
100x-500+135x=5x^2-25x
5x^2-260x+500=0
/5
x^2-52x+100=0
x^2-50x-2x+100=0
x(x-50)-2(x-50)=0
(x-50)(x-2)=0
x=2 OR 50 km/h
speed = 50 m/h
...
m.ananth@hotmail.ca
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Miscellaneous_Word_Problems/358409: Johnny has $100 now and saves $10 every month. His brother Jimmy has no money
currently and is going to save $15 per month. In how many months will Jimmy have
as much money as Johnny?
1 solutions
Answer 255778 by mananth(12270) on 2010-10-19 05:19:48 (Show Source):
You can put this solution on YOUR website!johnny 100 + 10 /month
Jimmy 15 /month
let them have same amount after x months
...
100+10x=15x
15x-10x=100
5x=100
x= 20 months
...
m.ananth@hotmail.ca
..
check
15*20=300
20*10+100=300
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Miscellaneous_Word_Problems/358411: Mary and Jane work part time for a library. Mary works every third day; Jane works
every fifth day. Today, they are both working together. In how many days will they
be working together again?
1 solutions
Answer 255777 by mananth(12270) on 2010-10-19 05:16:12 (Show Source):
You can put this solution on YOUR website!mary works third day
Jane works 5th day.
the leaset common multiple is 3*5 = 15
today they are working together
so they will work in the 1+15 = 16th day together
...
m.ananth@hotmail.ca
|
Numbers_Word_Problems/358417: find 3 consecutive even numbers such as that sum of the first and the third consecutive even numbers is equal to the second increased by 50
1 solutions
Answer 255775 by mananth(12270) on 2010-10-19 05:02:08 (Show Source):
You can put this solution on YOUR website!find 3 consecutive even numbers such as that sum of the first and the third consecutive even numbers is equal to the second increased by 50
...
let the consequtive even numbers be x,x+2,x+4
x+x+4=x+2+50
2x+4=x+52
2x-x=48
x=48
..
the numbers are 48,50,52
...
m.ananth@hotmail.ca
|
Travel_Word_Problems/358385: An airplane flying north at 200 mph passed over a point on the ground at 2:00 PM. Another airplane at the same altitude passed over the point at 2:30 PM, flying east at 400 mph. At what time were the planes 500 miles apart?
1 solutions
Answer 255773 by mananth(12270) on 2010-10-19 04:58:36 (Show Source):
You can put this solution on YOUR website!An airplane flying north at 200 mph passed over a point on the ground at 2:00 PM. Another airplane at the same altitude passed over the point at 2:30 PM, flying east at 400 mph. At what time were the planes 500 miles apart?
..
North plane 200 mph 2.00pm
East plane 400 mph 2.30 pm
...
in 1/2 hour north plan has traveled 100 miles. when other plane passes the point.
...
they are flying at right angles to each other.
when the east bound plane travels 2x miles north bound plane has traveled x+100 miles. ( because speed is half & it has 1/2 hour lead)
...
(2x)^(x+100)^2= 500^2
4x^2+x^2+200x+10000=250000
5x^2+200x-240000=0
5x^2+1200x-1000x-240000=0
5x(x+240)-1000(x+240)=0
(x+240)(5x-1000)=0
5(x+240)(x-200)=0
x=200 miles
2x=400 miles: speed = 400 mph
time = distance/speed
400/400 = 1 hour
....
CHECK
400^2+300^2=500^2
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Percentage-and-ratio-word-problems/358395: If two trains are 120 miles apart and are travelling toward each other at constant rate of 30mph and 40mph respectively.How far apart will they be exactly 1 hr before they meet.
1 solutions
Answer 255771 by mananth(12270) on 2010-10-19 02:24:37 (Show Source):
You can put this solution on YOUR website!If two trains are 120 miles apart and are travelling toward each other at constant rate of 30mph and 40mph respectively.How far apart will they be exactly 1 hr before they meet.
..
add up their speeds 40+30 = 70 mph.
they approach 70 miles towards each other in 1 hour.
they were 120 miles away.
120-70 = 50 miles.
they will be 50 miles away. after one hour.
...
m.ananth@hotmail.ca
|
Rectangles/358387: In a rectangle the lenght is 2cm longer than it's width & a diagonal is 10cm. What is the area??
PLease tell me the answer and how did u get it. ^^ tnx
1 solutions
Answer 255770 by mananth(12270) on 2010-10-19 02:21:34 (Show Source):
You can put this solution on YOUR website!In a rectangle the lenght is 2cm longer than it's width & a diagonal is 10cm. What is the area??
let the width be x cm
length = x+2 cm.
..
diagonal = 10 cm.
the diagonal and the sides of the rectangle form a right triangle with diagonal as the hypotenuse.
use pythagoras theorem
.
leg1^2+leg2^2= hypo^2
x^2+(x+2)^2= 10^2
x^2+x^2+4x+4 = 100
2x^2+4x+4-100=0
2x^2+4x-96=0
/2
x^2+2x-48=0
x^2+8x-6x-48=0
x(x+8)-6(x+8)=0
(x+8)(x-6)=0
x=6 which is positve
width 6 cm
length = 8 cm.
Area = L*W
Area = 6*8=48 cm^2
...
m.ananth@hotmail.ca
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Equations/358356: A leather coin purse has the shape of a triangle. Two sides are equal in length and the third side is 3cm shorter than one and one half times the length of the equal sides. the perimeter is 28.5 cm. find the lengths of the sides.
1 solutions
Answer 255756 by mananth(12270) on 2010-10-18 23:42:53 (Show Source):
You can put this solution on YOUR website!let the equal sides be x
the third side = x/2-3
..
x+x+x/2 -3=28.5
5x/2 = 28.5+3
5x/2=31.5
5x=63
/5
x=63/5
x=12.6 cm the equal sides
third side = 6.3
...
m.ananth@hotmail.ca
|
Travel_Word_Problems/358377: a boat takes 3 hours to go 24 miles upstream.it can go 36 miles downstream in the same time,Find the speed of the current and the speed of the boat in still water if x=the speed of the boat in still water and y=the speed of the current.
1 solutions
Answer 255753 by mananth(12270) on 2010-10-18 23:36:49 (Show Source):
You can put this solution on YOUR website!a boat takes 3 hours to go 24 miles upstream.it can go 36 miles downstream in the same time,Find the speed of the current and the speed of the boat in still water if
x=the speed of the boat in still water
y=the speed of the current.
downstream speed = x+y
upstream speed = x-y
...
time downstream = 36/(x+y)=3
3x+3y=36
time upstream = 24/(x-y)=3
3x-3y=24
add the equations
6x=60
/6
x= 10 mph speed of boat
...
plug value of x in equation
30+3y=36
3y=36-30
3y=6
y=2 mph speed of current
...
m.ananth@hotmail.ca
|
Money_Word_Problems/358362: debra invested $18000.Part of it was invested at 3% annual simple interest, and the rest was invested at 4%. Her interest income for the first year was $650.How much did she invest at each rate?
1 solutions
Answer 255747 by mananth(12270) on 2010-10-18 23:22:45 (Show Source):
You can put this solution on YOUR website!debra invested $18000.Part of it was invested at 3% annual simple interest, and the rest was invested at 4%. Her interest income for the first year was $650.How much did she invest at each rate?
...
$x @ 3%
18000-x@4%
Interest = 650
...
3x+4(18000-x)=65000
3x+72000-4x=65000
-x=-7000
x= $7000 @ 3%
balance $11000 @4%
...
m.ananth@hotmail.ca
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Linear-equations/358364: Find the equation( in slope intercept form)of the line passing through the points given coordinates(-4,0) ,(-1,2)
1 solutions
Answer 255743 by mananth(12270) on 2010-10-18 23:17:09 (Show Source):
You can put this solution on YOUR website!slope = y2-y1/x2-x1
=2-0/-1-(-4)
=2/3
...
y=mx+b
Take any point (-4,0)
plug x,y,m to get b
0=2/3*-4 +b
0=-8/3
b= 8/3
...
equation = y=(2x/3)+8/3
...
m.ananth@hotmail.ca
|
Geometry_Word_Problems/358367: a building casts a shadow 40 ft long when the sun's angle of elevation is 58 degrees. Find the height of the building.
1 solutions
Answer 255741 by mananth(12270) on 2010-10-18 23:07:12 (Show Source):
You can put this solution on YOUR website!a building casts a shadow 40 ft long when the sun's angle of elevation is 58 degrees. Find the height of the building.
...
let the height of building be x
tan(58 degrees) = x/40
1.60033453 = x/40
x = 1.60033453 * 40
x = 64.01 feet
...
m.ananth@hotmail.ca
|
Linear-systems/358365: I need help with a linear word problem and equation (Please explain how you got your answer because I'm confused. Thank you.):
Fundrasing: To raise money, your student council is selling magazine subscriptions. The student council will receive a one-time bonus of $150 from the magazine publisher plus 38% of the subscription money. The following verbal model represents the situation. Write a linear equation from the verbal model.
Money = Bonus + Subscription . Subscription
Raised Percentage Money
What I got was m=150+0.38x.
One more thing:
How much subscription money is needed for the council to raise a total of $300? Round your answer to the nearest dollor.
1 solutions
Answer 255740 by mananth(12270) on 2010-10-18 23:03:41 (Show Source):
You can put this solution on YOUR website!
To raise money, your student council is selling magazine subscriptions. The student council will receive a one-time bonus of $150 from the magazine publisher plus 38% of the subscription money. The following verbal model represents the situation. Write a linear equation from the verbal model.
let the subscription be x
they recieve 38% of the
per subscription they receive 0.38x
M = 150+0.38x
300=150+0.38x
-150
300-150=0.38x
150=0.38x
/0.38
150/0.38=x
$3947 is the subscription money required
...
m.ananth@hotmail.ca
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Miscellaneous_Word_Problems/358305: Pop's Cycle Shop sells bicycles and tricycles. The number of bicycles is 1 less than 4 times the number of tricycles. All the bicycles and tricycles together have a total of 174 wheels. How many bicycles are there?
1 solutions
Answer 255693 by mananth(12270) on 2010-10-18 21:19:42 (Show Source):
You can put this solution on YOUR website!let tricycles be x
bicycles= 4x-1
...
3x+2(4x-1)=174
3x+8x-2=174
11x=174+2
11x=176
x=16 tricycles
bicycles = 4x-1=64-1
= 63 bicycles
...
m.ananth@hotmail.ca
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Geometry_Word_Problems/358301: Lois rode her bike to visit a friend. She traveled 10 mi/h. While she was there, it started to rain. Her friend dorve her home in a car traveling 20 mi/h. Lois took 1.5 h longer to go to her friend's than to return home. How many hours did it take Lois to ride to her friends house?
MY WORK-
r t d
10 mi/h 1.5+t 10(1.5+t)
20 mi/h t 20t
10(1.5+t)=20t
10(1.5+t)=20t
15+10t=20t
15+10t-10t=20t
15=10t
1 solutions
Answer 255689 by mananth(12270) on 2010-10-18 21:13:24 (Show Source):
You can put this solution on YOUR website!Lois rode her bike to visit a friend. She traveled 10 mi/h. While she was there, it started to rain. Her friend dorve her home in a car traveling 20 mi/h. Lois took 1.5 h longer to go to her friend's than to return home. How many hours did it take Lois to ride to her friends house?
...
let the time to friends house be x hours
speed = 10 mph
distance = 10x
...
return
speed = 2o mph
time = x-1.5
distance = 20*(x-1.5)
...
10x=20(x-1.5)
10x=20x-30
10x-20x=-30
-10x=-30
/-10
x= 3 hours
...
m.ananth@hotmail.ca
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Matrices-and-determiminant/358296: How do you solve the system equation?
6a+ 2b= 11
3a= 8b+ 1
1 solutions
Answer 255687 by mananth(12270) on 2010-10-18 21:05:24 (Show Source):
You can put this solution on YOUR website!6a+ 2b= 11
3a= 8b+ 1
re write this equation.
3a-8b=1
multiply by -2 and it to first equation to eliminate x
-6a+16b=-2
add
6a-6a+2b+16b=11-2
18b=9
divide by 9
2b=1
/2
b = 1/2
..
plug value of b in second equation
3a=4+1
3a=5
divide by 3
a= 5/3
...
m.ananth@hotmail.ca
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Proportions/358266: how do you multiply y?
for example:
5y * y?
1 solutions
Answer 255666 by mananth(12270) on 2010-10-18 20:34:40 (Show Source):
You can put this solution on YOUR website!In multiplication of terms you multiply the co-efficients and
use the law of indices .( add up the power of the variables)
2y*2y = 2*2*y*y = 4y^2
...
3x*6x^2 = 3*6*x*x*x = 18x^3
...
2a^2*3b= 2*3*a*a*b = 6a^2b
...
m.ananth@hotmail.ca
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Linear_Equations_And_Systems_Word_Problems/357888: A person deposited $500 in a savings account that pays 5% annual interest that is compounded yearly. At the eand of 10 years, how much money will be in the savings account?
1 solutions
Answer 255465 by mananth(12270) on 2010-10-18 10:36:38 (Show Source):
You can put this solution on YOUR website!A person deposited $500 in a savings account that pays 5% annual interest that is compounded yearly. At the eand of 10 years, how much money will be in the savings account?
...
a=p(1+r/n)^nt
a=500*(1+0.05)^10
a= $814.4
...
m.ananth@hotmail.ca
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