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i need help solving this problem.
1 solutions
Answer 297829 by mananth(12270)   on 2011-03-29 02:30:26 (Show Source):
You can put this solution on YOUR website!Below an interest of Rs 2400 one investment becomes negative. not possible
I have worked with Rs. 2550. as interest. instead of Rs 2250.
Part I 8.00% per annum
Part II 10.50% per annum
x + y 30000 ------------------------1
8.00%x+10.50%y= Rs2,550.00
Multiply by 100
8x+10.5y =Rs255,000.00 --------2
Multiply (1) by -8
we get
-8x-8y= -240000.00
Add this to (2)
2.5y=$15,000.00
divide by 2.5
y=Rs.6,000.00 investment at at 10.5%
Balance Rs.24,000.00 investment at 8%
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Travel_Word_Problems/428493: Two cars leave towns 750 kilometers apart at the same time and travel toward each other. One car's rate is 10 kilometers per hour less than the other's. If they meet in 5 hours, what is the rate of the slower car?
I have no idea how to even start this problem. Is there an equation or what do I do to solve this?
1 solutions
Answer 297828 by mananth(12270) on 2011-03-29 02:09:52 (Show Source):
You can put this solution on YOUR website!Car A x mph
Car B x+ 10
..
They are going away from each other.
So add up their speed.
combined speed = x+ 1 x + 10
( 2 x + 10 )
Time = 5 hours
Distance = 750 miles
Distance = speed * time
( 2 x 10 )* 5 = 750
10 x + 50 = 750
10 x = 750 + -50
10 x = 700
/ 10
x= 70 mph Car A
Car B 70 + 10 = 80 mph
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Linear_Equations_And_Systems_Word_Problems/428523: One pump can empty a pool in 5 days, whereas a second pump can empty the pool in 7 days. How long will it take the two pumps, working together, to empty the pool?
1 solutions
Answer 297827 by mananth(12270) on 2011-03-29 01:55:36 (Show Source):
You can put this solution on YOUR website!Emptying the tank is one job
one pipe drains in 5 days
It does 1/ 5 of the job in 1 day
other pipe 7 day
It does 1/ 7 of thejob in 1 day
Together they will do 1/5+ 1/ 7
Together they will do 12/35 of the job in one day
So they will take 2 8/9 days
So they will take 2.92 days
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Mixture_Word_Problems/428518: How many liters of distilled water must be added to 140 liters of an 80% alcohol solution to obtain a 70% solution? i think the answer is 2.3 liters.
1 solutions
Answer 297826 by mananth(12270) on 2011-03-29 01:50:04 (Show Source):
You can put this solution on YOUR website!------ Percent ---------------- quantity
Alcohol 80 ---------------- 140
water 0 ---------------- x
Total 70 ---------------- 140+x
80*140+ 0*x=70(140+x)
11200=9800+70x
-70x=9800-11200
-70x=-1400
/-70x
x=20 gallons water
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Miscellaneous_Word_Problems/428525: An airplane can travewl 380 miles into the wind in the same time that it can travel 420 miles with the wind. If the wind speed is 10 miles per hour, find the speed of the airplane without any wind.
1 solutions
Answer 297825 by mananth(12270) on 2011-03-29 01:41:55 (Show Source):
You can put this solution on YOUR website!plane speed x mph
wind speed 10 mph
..
against wind x-10mph
with wind x+10 mph
Distance against wind 380
Distance with tail wind 420
Time = same
380/(x- 10)= 420/(x+ 10)
380*(x+ 10)= 420*(x- 10)
380x +3800 =420x-4200
420x -380x =4200+3800
40x =8000
/40
x= 200 mph
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Linear_Equations_And_Systems_Word_Problems/428528: Two cars leave town at the same time and travel in the same direction. One car travels one and one-half times as fast as the other car. After 4 hours and 45 minutes, they are 95 miles apart. What is the speed of each car?
I don't want you to solve it, I am looking for the two equations for me to solve the linear system.
1 solutions
Answer 297824 by mananth(12270) on 2011-03-29 01:31:53 (Show Source):
You can put this solution on YOUR website!Car A x mph
Car B 1.5 x mph
..
same direction
subtract the speed
resultant speed = 1.5x-x= 0.5x
time = 4 3/4 hour = 4.75
distance = 95 miles
d/speed = time
95/0.5x= 4.75
95 = 2.375x
x=95/2.375
40 mph Car A
Car B = 60 mph
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Linear_Equations_And_Systems_Word_Problems/428527: I just need help setting this up, I can solve it after that.
At a Conseesion stand, five hotdog(s) and two hamburger(s) cost $9.75; two hotdog(s) and five hamburger(s) cost $11.25, Find the cost of one hotdog and one hamburger.
1 solutions
Answer 297823 by mananth(12270) on 2011-03-29 01:24:53 (Show Source):
You can put this solution on YOUR website!5x+2y=9.75 .............1
2x+5y=11.25 .............2
multiply (1)by -5
Multiply (2) by 2
-25x-10y =-48.75
4x+10y=22.5
Add the two equations
-21x=-26.25
/-21
x=1.25 hotdog cost
plug value of x in (1)
5x+2y=9.75
6.25+2y= 9.75
2y=9.75 -6.25
2y=3.5
y=1.75 hamburger cost
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Mixture_Word_Problems/428511: How much pure acid should be mixed with 6 gallons if a 60% acid in order to get a 70% acid solution
1 solutions
Answer 297818 by mananth(12270) on 2011-03-28 23:37:02 (Show Source):
You can put this solution on YOUR website!.......... Percent ---------------- quantity
Solution ..........60----------------30
Pure acid.........100----------------x
Total 70 ---------------- 30+x
60*6+100 *x=70(6+ x)
360+100x =420+70x
100x-70 x=420-360
30x=60
/30
x=2 gallons 100 % Pure acid
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Money_Word_Problems/428429: Carl invested $10,000, part in a CD paying 8.5% annual interest, the rest in a mutual fund paying 7% annual interest. The annual income from the CD is $200 more than the annual income from the mutual fund. How much money was put into each type of investment?
1 solutions
Answer 297802 by mananth(12270) on 2011-03-28 21:44:49 (Show Source):
You can put this solution on YOUR website!Part I 8.50% per annum
Part II 7.00% per annum
x+y=10000 ------------------------1
8.50%x-7.00%y=$200.00
Multiply by 100
8.5x-7y =$20,000.00--------2
Multiply (1) by -8.5
we get
-8.5x-8.5y=-85000.00
Add this to (2)
x-15.5y =-$65,000.00
divide by -15.5
y=$4,193.55 investment at7.00%
Balance $5,806.45 investment at 8.50%
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Mixture_Word_Problems/428386: how much pure gold (24k) must be mixed with 60% gold to get 20 grams of 75% gold
1 solutions
Answer 297786 by mananth(12270) on 2011-03-28 21:03:25 (Show Source):
You can put this solution on YOUR website!......... percent ---------------- quantity
24k 100---------------- x gms
Gold 60% 60---------------- 20-x gms
Total 75.00% ---------------- 20
100x+60(20-x)=75*20
100x+1200-60x=1500
100x-60x =1500-1200
40x=300
/40
x=7.5gms
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Linear-equations/428412: equation for the line that passes through the point (-1, 2) and is parallel to the line with equation 2y+6x=10
1 solutions
Answer 297783 by mananth(12270) on 2011-03-28 20:50:53 (Show Source):
You can put this solution on YOUR website!6x+2y=10
Find the slope of this line 2
y=-6x+10
Divide by 2
y =-3x+ 5
Compare this equation with y=mx+b
slope m =-3
The slope of a line parallel to the above line will be the same
The slope of the required line will be -3
m=-3,point(-1,2 )
Find b by plugging the values of m & the point in
y=mx+b
2=3.00+ b
b=-1
m=-3
Plug value of the slope and b
The required equation is y=-3x-1 point (-1, 2) and is parallel to the line with equation 2y+6x=10
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Linear-equations/428398: bob has 60 coins consisting of quarters and dimes. The coins combined value is $9.45. Find out how many are quarters and how many are dimes
1 solutions
Answer 297781 by mananth(12270) on 2011-03-28 20:43:31 (Show Source):
You can put this solution on YOUR website! quarters ------------ x
dimes ------------ y
1 x + 1 y = 60 .............1
25 x + 10 y = 945 .............2
multiply (1)by -10
Multiply (2) by 1
-10 x + -10 y = -600
25 x + 10 y = 945
Add the two equations
15 x=345
/15
x=23 quarters
plug value of x in (1)
x+y=60
23+y=60
y = 60 + -23
y = 37 dimes
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Miscellaneous_Word_Problems/428106: The speed of a stream is 3 mph. A boat travels 5 miles upstream in the same time it takes to travel 11 miles downstream. What is the speed of the boat in still water?
Any insight please.
1 solutions
Answer 297624 by mananth(12270) on 2011-03-28 11:05:07 (Show Source):
You can put this solution on YOUR website!boat speed x mph
current speed 3 mph
..
against current x - 3 mph
with current x + 3 mph
Distance upstream= 5
Distance downstream= 11
Time = same
5 /(x- 3 )= 11 /(x+ 3 )
5 *(x+ 3 )= 11 *(x- 3 )
5 x + 15 = 11 x -33
11 x -5 x = 33 + 15
6 x = 48
/ 6
x= 8 mph
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percentage/428076: Hi, I need your help on this question:
In a fish shop,60% of the fish were guppies and the rest were angelfish. After 81 fishes were removed, the number of guppies decreased by 25% and the number of angelfish was 1/4 of the original number of angelfish.
a)How many guppies were removed?
b)How many angelfish were there at first?
Thank you, I really appreciate your help!
1 solutions
Answer 297623 by mananth(12270) on 2011-03-28 10:54:11 (Show Source):
You can put this solution on YOUR website!In a fish shop,60% of the fish were guppies and the rest were angelfish. After 81 fishes were removed, the number of guppies decreased by 25% and the number of angelfish was 1/4 of the original number of angelfish.
a)How many guppies were removed?
b)How many angelfish were there at first?
Thank you, I really appreciate your help!
let total fish be x
0.6x = guppies
0.4x = angelfish
..
x-81 = 0.75*0.6x +0,25*0.4x
x-81=0.45x+0.1x
x-81=0.55x
0.45x=81
x=180 fish
60 % of 180 = 108 were guppies
40%of 180= 72 were angel fish
...
25%of 108 = 27 guppies were removed
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Money_Word_Problems/428064: When Sara Whitehorse changed jobs, she rolled over the $7700.00 in her retirement account into two simple interest accounts. On one account, the annual simple interest rate is 8%, and on the second account, the annual simple interest is 6%. How much must be invested in each account if the two accounts earned the same amount of annual interest?
1 solutions
Answer 297610 by mananth(12270) on 2011-03-28 09:33:15 (Show Source):
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Travel_Word_Problems/428027: An airplane flew for 6 hours at a speed of 455 miles per hour and then
for 5 more hours at a speed of x miles per hour. The average speed of
the airplane was 495 miles per hour. Write an equation that could be
used to find x.
1 solutions
Answer 297604 by mananth(12270) on 2011-03-28 09:23:41 (Show Source):
You can put this solution on YOUR website!6 hours at 455 mph = 2730 miles
5 hours at x mph distance = 5x
..
Total distance = 5x+2730
Total time = 11 hours
Average speed = (5x+2730)/11 mph
495 = (5x+2730)/11
495*11= 5x+2730
5x=5445-2730
5x=2715
x=543
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Expressions-with-variables/428063: I am supposed to solve using the substitution method.
5x-6y=-20
5x+45=y
Here is what I have tried and I think it is wrong.
I switched the 2nd equation so that it read y=5x+45.
It was then,
5x-6y=-20
y=5x+45
Here is how I worked it out
5x-6(5x+45)=-20
5x-30x-270=-20
-35x-270+270=-20+270
-35x=250 and I divided both sides by -35 and got 7.14 but I know this is wrong and I do not know where or what I did wrong.
1 solutions
Answer 297601 by mananth(12270) on 2011-03-28 09:01:42 (Show Source):
You can put this solution on YOUR website!5x-6y=-20
5x+45=y
5x-6y=-20 .............1
y=45+5x ---------2
plug the value of y in (1)
5x-6(45+ 5x)=-20
5x-270-30x=-20
5x-30x=-20+270
-25x=250
/-25
x=-10
Plug the value of x in (1)
5x-6y=-20
5*-10-6y =-20
-50-6y=-20
-6y=30
/-6
y=-5
CHECK
y=45+5x
-5=45-50
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Numbers_Word_Problems/427991: Two numbers are in the ratio 1:3. If i add 2 to each of the numbers, the ratio becomes 1:2. Find the number. PLease write it in the form of algebraic equation.
Thank You!
1 solutions
Answer 297581 by mananth(12270) on 2011-03-28 04:44:40 (Show Source):
You can put this solution on YOUR website!Let one number be x
let other number be y
x/y = 1/3
cross multiply 3 x = 1 y
3x -y =0 ...........1
( X +2)/(y+2)= ½
2(x+2)= 1(y+2)2x+4=y+2
2x-y=-2 ............2
Multiply (1) by -1 we get
-3x-y=0 ............3
Add (3)&(2)
-x=-2
x=2
2 & 6
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Miscellaneous_Word_Problems/428009: The speed of a stream is 5mph. A boat travels 5 miles upstream in the same time it takes to travel 15 miles downstream. What is the speed of the boat in still water.
help please.
1 solutions
Answer 297580 by mananth(12270) on 2011-03-28 04:40:04 (Show Source):
You can put this solution on YOUR website!boat speed x mph
current speed 5 mph
..
against current x - 5 mph
with current x + 5 mph
Distance against current 5
Distance with current 15
Time = same
5 /(x- 3 )= 15 /(x+ 3 )
5 *(x+ 3 )= 15 *(x- 3 )
5 x + 15 = 15 x -45
15 x -5 x = 45 + 15
10 x = 60
/ 10
x= 6 mph
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Miscellaneous_Word_Problems/428014: A plane flies 435 miles with the wind and 345 miles against the wind in the same length of time. If the speed of the wind is 15mph, find the speed of the plane in still air.
1 solutions
Answer 297579 by mananth(12270) on 2011-03-28 04:34:20 (Show Source):
You can put this solution on YOUR website!let speed in still air be x mph
wind speed 10 mph
..
against wind x - 10 mph
with wind x + 10 mph
Distance against wind 345
Distance with tail wind 435
Time = same
345 /(x- 3 )= 435 /(x+ 3 )
345 *(x+ 3 )= 435 *(x- 3 )
345 x + 1035 = 435 x -1305
435 x -345 x = 1305 + 1035
90 x = 2340
/ 90
x= 26 mph
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Linear_Equations_And_Systems_Word_Problems/428026: A scientist has one alloy containing 39% copper and another containing 61% copper. How many pounds of each alloy must he use to make 41 pounds of a third alloy containing 48% copper?
1 solutions
Answer 297577 by mananth(12270) on 2011-03-28 04:20:13 (Show Source):
You can put this solution on YOUR website!.........percent ---------------- quantity
Alloy 1 39 ---------------- x pounds
Alloy 2 61 ---------------- 41-x pounds
Total 48% ---------------- 41
39x+61(41-x)=48* 41
39x+2501 -61x=1968
39x-61x= 1968-2501
-22x=-533
/-22
x=24.23 pounds 39.00%
16.77 pounds 61.00%
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Travel_Word_Problems/428032: A pilot flies 500 miles against a
20-mile-per-hour wind. On the next day, the pilot
flies back home with a 10-mile-per-hour tail wind.
The total trip (both ways) takes 4 hours. Find the
speed of the airplane without a wind.
1 solutions
Answer 297574 by mananth(12270) on 2011-03-28 04:12:56 (Show Source):
You can put this solution on YOUR website!plane speed in still air x
wind speed 20
against wind x- 10
with wind x+10
Distance= 500 miles
Time agianst + time with wind =4 hours
t=d/r
500/(x+20)+500/(x-20)= 4
LCD = (x-20)(x +20)
500*(x-20)+500(x+20)=4
500x-10000+500x+10000=4x ^2-400
1000x=4x ^2-400
4x^2-1000x-400=0
Find the roots of the equation by quadratic formula
a= 4 b= -1000 c= -400
b^2-4ac= 1000000 - 6400
b^2-4ac= 1006400
x1=(1000+1003.19 )/8
x1= 250.4 mph
x2=(1000-1003.19) /8
x2=-0.4
Ignore negative value
250.4 mph =speed in still air
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Mixture_Word_Problems/427993: A silversmith mixed 25 g of a 60% silver alloy with 40 g of a 5% silver alloy. What is the percent concentration of the resulting alloy? (Round to the nearest tenth of a percent.)
%
1 solutions
Answer 297555 by mananth(12270) on 2011-03-27 23:29:26 (Show Source):
You can put this solution on YOUR website! percent ---------------- quantity
alloy 60 ---------------- 25 gms
alloy 5 ---------------- 40 gms
Total x ---------------- 65 gms
60*25+5* 40=65x
1500+200 =65x
1700=65x
/65
1700/65= x
26.15=x
26.5% mix
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Length-and-distance/427989: it takes a passenger train 5 hr less time than it takes a freight train to make the trip from hughesville to rockville. the passenger train averages 105km/h while the freight train averages 70 km/h find the distance from rockville to hughesville.
1 solutions
Answer 297552 by mananth(12270) on 2011-03-27 23:18:07 (Show Source):
You can put this solution on YOUR website!the trip from hughesville to rockville. the passenger train averages 105km/h while the freight train averages 70 km/h find the distance from rockville to hughesville.
distance = x
time freight train = x/70
time passenger train = x/105
x/70-x/105 = 5
LCD = 7350
105x-70x= 7350*5
35x=36750
/35
x=36750/35
x= 1050 km
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Linear-systems/427984: 0.1x+0.7y=-2.3
0.3x-0.2y=2.3
solve the system using substitution method
1 solutions
Answer 297547 by mananth(12270) on 2011-03-27 23:02:44 (Show Source):
You can put this solution on YOUR website!0.1x+0.7y=-2.3
0.3x-0.2y=2.3
multiply both equations by 10
x+7y=-23
3x-2y=23
x+7y=-23 .............1
-2y=23-3 x---------2
/-2
y=-11.5- 1.5x
Plug the value of y in (1)
x+7(-11.5+1.5x)= -23
x-80.5+10.5x)=-23
x+10.5x= -23
11.5x=57.5
/11.5
x=5
Plug the value of x in (1)
x+7y=-23
5+7y=-23
5+7y=-23
7y=-28
/7
y=-4
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Travel_Word_Problems/427544: the speed of a stream is 3 mph. A boat travels 3 miles upstream in the same time it takes to travel 9 miles downstream. What is the speed of the boat in still water?
1 solutions
Answer 297383 by mananth(12270) on 2011-03-27 09:32:44 (Show Source):
You can put this solution on YOUR website!let speed in still water = x mph
current speed 3 mph
..
upstream speed = x-3 mph
downstream speed = x+3 mph
Distance upstream=3
Distance downstream=9
Time = same
3/(x-3)= 9/(x+3)
3*(x+3)= 9*(x-3)
3x+3=9x-27
9x-3x=27 +3
6x=30
/6
x=5mph
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Travel_Word_Problems/427609: a biker can travel at a speed of x km/h over a distance of 15km. if the biker reduces his speed by 2km/h he will only manage to travel 10km for the same time Calculate x
1 solutions
Answer 297374 by mananth(12270) on 2011-03-27 09:09:20 (Show Source):
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Rational-functions/427563: Please help me set up this problem:
"Tim paddled his kayak 12 km upstream against a 3 km/hour current and back again in 5 hours and 20 minutes. In that time how far could he have paddled in still water?"
1 solutions
Answer 297365 by mananth(12270) on 2011-03-27 08:21:31 (Show Source):
You can put this solution on YOUR website!
speed in still water = r
current speed =3
upstream speed = r-3
downstream speed = r+3
Distance= 12 miles
Time upstream + time downstream = 5.33 hours
12/(r+3) +12/(r-3 )=5.33
LCD = (r-3)(r+ 3)
12*(r-3) +12(r+3 )= 5.33
12r-36r+12r+36=5.33
r^2-24r=5.33r^2-47.97
5.33r^2- 24r-47.97
Find the roots of the equation by quadratic formula
a=5.33 b=-24 c=-47.97
b^2-4ac= 576+1022.72
b^2-4ac= 1598.72
x1=(24+ 39.98)/ 10.66
x1= 6
x2=(24-39.98) /10.66
x2= -1.5 ( ignore)
Speed = 6 mph
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