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My daughter is twice as old as my son. My wife is three times as old as the sum of the ages of my son and daughter, and I am as old as my wife and my daughter. My mother whose age is the total of all our ages is now 69.
1 solutions
Answer 265357 by mananth(12270)   on 2010-11-17 10:33:44 (Show Source):
You can put this solution on YOUR website!what is the age of my daughter?
My daughter is twice as old as my son. My wife is three times as old as the sum of the ages of my son and daughter, and I am as old as my wife and my daughter. My mother whose age is the total of all our ages is now 69.
..
let daughter's age be x
son = x/2
wife = 3(x+x/2)
my age= x+3(x+x/2)
mother=(x+x/2)+3(x+x/2)+x+3(x+x/2)=69
..
(x+x/2)(1+3+3)+x=69
7(x+x/2)+x=69
7*3x/2 +x=69
21x/2+x=69
21x+2x /2=69
23x=138
x=138/23
x= 6 daughter's age
...
m.ananth@hotmail.ca
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Travel_Word_Problems/372512: if you are traveling 45 miles per hour how much distance do you cover in 3 seconds, to the nearest foot?
1 solutions
Answer 265318 by mananth(12270) on 2010-11-17 08:33:08 (Show Source):
You can put this solution on YOUR website!45 miles per hour how much distance do you cover in 3 seconds,
...
1 mph = 1.466 ft/second
45 mph = 45*1.466
= 66 ft/second
in 3 seconds it will travel = 66*3= 198 feet.
...
m.ananth@hotmail.ca
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Expressions-with-variables/372486: Mr.Engen rented a car for $35.00 a day an $0.45 per mile. He had the car for two days and paid $166.75 How many miles did he drive?
1 solutions
Answer 265311 by mananth(12270) on 2010-11-17 07:14:34 (Show Source):
You can put this solution on YOUR website!Mr.Engen rented a car for $35.00 a day an $0.45 per mile. He had the car for two days and paid $166.75 How many miles did he drive?
..
$35 per day
2 days = 70
let the miles be x
cost per mile = 0.45
70+0.45x= 166.75
0.45x= 166.75-70
0.45x=96.75
/0.45
x= 96.75/0.45
x =215 miles
...
m.ananth@hotmail.ca
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Quadratic_Equations/372487: I need to use quadratic equations to find two real numbers that satisfy the sum of 15 and the product 36
1 solutions
Answer 265309 by mananth(12270) on 2010-11-17 07:10:30 (Show Source):
You can put this solution on YOUR website!x+y =15
xy = 36
x= 36/y
..
plug value of x in the first equation
36/y +y =15
(36+y^2)/y =15
36+y^2 =15y
y^2-15y+36=0
...
y^2-12x-3x+36=0
y(y-12)-3(y-12)=0
(y-12)(y-3)=0
y =12 OR y =3
...
m.ananth@hotmail.ca
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Age_Word_Problems/372482: Manuel Anselmo is ten times older than his son, Andrew. In 20 years, Manuel's age will be 4 more than twice Andrew's age. How old was he when Andrew was born?
1 solutions
Answer 265307 by mananth(12270) on 2010-11-17 07:05:48 (Show Source):
You can put this solution on YOUR website!Andrew = x
father = 10x
..
after 20 years
--------------
son x+20
father 10x+20
..
10x+20 = 2(x+20)+4
10x+20=2x+40+4
10x-2x=40-20+4
8x=24
/8
x= 3 andrew's age now
father's age = 3x = 30
..
3 years ago when andrew was born father was 30-3= 27 years.
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m.ananth@hotmail.ca
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Linear-systems/372474: solve system of equations using multiplication with the addition method;
7x-3y=-5
3x+2y=11
1 solutions
Answer 265302 by mananth(12270) on 2010-11-17 06:04:51 (Show Source):
You can put this solution on YOUR website!7x-3y=-5....................1
3x+2y=11....................2
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multiply (1) by 2 & (2) by 3
14x-6y=-10
9x+6y=33
..
add them up
14x+9x=-10+33
23x=23
/23
x=1
..
plug value of x in (1)
7-3y=-5
3y=7+5
3y=12
/3
y=4
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m.ananth@hotmail.ca
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Miscellaneous_Word_Problems/372477: The attendance at a scholol variety show was 578 people. A ticket for the lower box is worth 75 and a ticket for the upper box is worth 40. If the total revenue is 29,295,about how many tickets were sold for the lower box?
(Ans. algebrically)
1 solutions
Answer 265300 by mananth(12270) on 2010-11-17 05:55:56 (Show Source):
You can put this solution on YOUR website!lower box - x tickets --------------75 pesos
upper box -578-x tickets------------40 pesos
..
total collection = 29,295
..
75x+40(578-x)=29,295
75x+23,120-40x=29,295
35x+23120=29295
35x=29,295-23120
35x=6175
x=6175/35
x= 176 tickets
...
you can also set up a linear system
x+y = 578
75x+40y = 29295
...
m.ananth@hotmail.ca
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Miscellaneous_Word_Problems/372478: A vending machine for canned soda takes only 5 and 10 coins. There are five times as many 10 peso coins than 5 peso coins in the machine. The total value of the coins is 440 pesos. How many of each kind are there?
1 solutions
Answer 265299 by mananth(12270) on 2010-11-17 05:53:51 (Show Source):
You can put this solution on YOUR website!5 peso coins ------------- x
10 peso coins -------------5x
..
Value = 440
..
5x+10*5x=440
5x+50x=440
55x= 440
/55
x= 8--- 5 peso coins
5x = 5*8 = 40-- 10 peso coins
...
m.ananth@hotmail.ca
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Miscellaneous_Word_Problems/372479: The attendance at a scholol variety show was 578 people. A ticket for the lower box is worth 75 peos and a ticket for the upper box is worth 40 pesos. If the total revenue is 29,295 pesos,about how many tickets were sold for the lower box?
1 solutions
Answer 265298 by mananth(12270) on 2010-11-17 05:48:45 (Show Source):
You can put this solution on YOUR website!lower box - x tickets --------------75 pesos
upper box -578-x tickets------------40 pesos
..
total collection = 29,295
..
75x+40(578-x)=29,295
75x+23,120-40x=29,295
35x+23120=29295
35x=29,295-23120
35x=6175
x=6175/35
x= 176 tickets
...
you can also set up a linear system
x+y = 578
75x+40y = 29295
...
m.ananth@hotmail.ca
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Numbers_Word_Problems/372443: Two positive numbers have a difference of 2. Their reciprocals have a sum of 20/21. What are the numbers?
1 solutions
Answer 265292 by mananth(12270) on 2010-11-17 02:53:59 (Show Source):
You can put this solution on YOUR website!let the numbers be x
the other number will be x+2
1/x + 1/(x+2) = 20/21
((x+2)+x)/x(x+2)= 20/21
(2x+2)/(x(x+2)= 20/21
21(2x+2)= 20x(x+2)
42x+42=20x^2+40x
20x^2-2x-42=0
/2
10x^2-x-21=0
10x^2-15x+14x-21=0
10x(x-1.5)+14(x-1.5)=0
(10x+14)(x-1.5)=0
10(x+1.4)(x-1.5)=0
(x+1.4)(x-1.5)=0
x =-1.4
OR
x=1.5
..
1.5 & 3.5
OR
-1.4 & 0.6
...
m.ananth@hotmail.ca
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Miscellaneous_Word_Problems/372451: One grocery clerk can stock a shelf in 35 min. A second clerk requires 40 min to stock the same shelf. How long would it take to stock the shelf if the two clerks worked together?
1 solutions
Answer 265291 by mananth(12270) on 2010-11-17 02:41:48 (Show Source):
You can put this solution on YOUR website!one clerk 35 minutes
other clerk 40 minutes
..
first clerk 1/35 of the job in 1 minute
second clerk 1/40 of the job in 1 minute
..
together they do 1/35 + 1/40 of the job in 1 minute
=(40+35)/40*35
=75/1400
=3/56 of the job in 1 minute
so they will take 56/3 = 18.66 hours together.
...
m.ananth@hotmail.ca
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Rate-of-work-word-problems/372466: Two pipes are used to fill an oil tanker. When the larger pipe is used alone, it takes 60 hours to fill the tanker. When the smaller pipe is used alone, it takes 80 hours to fill the tanker. The large pipe begins filling the tanker. After 20 hours, the large pipe is closed and the smaller pipe is opened. How much longer will it take to finish filling the tanker using only the smaller pipe?
1 solutions
Answer 265290 by mananth(12270) on 2010-11-17 02:37:16 (Show Source):
You can put this solution on YOUR website!Two pipes are used to fill an oil tanker. When the larger pipe is used alone, it takes 60 hours to fill the tanker. When the smaller pipe is used alone, it takes 80 hours to fill the tanker. The large pipe begins filling the tanker. After 20 hours, the large pipe is closed and the smaller pipe is opened. How much longer will it take to finish filling the tanker using only the smaller pipe?
..
larger pipe 60 hours
smaller pipe 80 hours
..
Larger pipe does 1/60 of the job in 1 hour
so in 20 hours it does 20/60 of the job .= 1/3 of the job.
..
balance job will be 1-1/3 = 2/3 of the job.
..
smaller pipe does 1/80 of the job in 1 hour
for 2/3 of the job it will take ?
(2/3) / (1/80)
2/3 *80
=160/3
=53.33 hours to do the remaining job of filling the tank.
...
m.ananth@hotmail.ca
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Mixture_Word_Problems/372467: Suppose that x liters of 30% acid solution are mixed with y liters of a 43% solution to obtain 100 L of a 40% solution. One equation is a system for solving this problem is x+y = 100. Which of the following is the other equation?
a. 0.43x+0.30y = 0.40*100
b. 30x+43y = 40
c. 0.30x+0.43y = 0.40*100
d. 43x+30y = 0.40*100
1 solutions
Answer 265289 by mananth(12270) on 2010-11-17 02:30:11 (Show Source):
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Travel_Word_Problems/372446: A cruise ship can sail 32 mph in calm water. Sailing with the Gulf Stream, the ship can sail 228 mi in the same amount of time as it takes to sail 156 mi against the Gulf Stream. Find the rate of the Gulf Stream.
1 solutions
Answer 265275 by mananth(12270) on 2010-11-17 01:28:18 (Show Source):
You can put this solution on YOUR website!A cruise ship can sail 32 mph in calm water. Sailing with the Gulf Stream, the ship can sail 228 mi in the same amount of time as it takes to sail 156 mi against the Gulf Stream. Find the rate of the Gulf Stream.
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rate of current be xmph
..
rate with current = 32+x : d= 228 miles
rate against current = 32-x: d=156 miles
..
times are same, so equate the time
..
228/(32+x)= 156/(32-x)
228x(32-x)=156(32+x)
7296-228x= 4992+156x
reorganise
228x+156x=7296-4992
72x= 2304
/72
x= 2304/72
x= 32 mph the rate of current
...
m.ananth@hotmail.ca
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Travel_Word_Problems/372402: plane travels 175 miles with the wind in the same amount of time it flew 150 miles against the wind. what was the speed of the plane in the still air if the wind was blowing at 20 mph?
1 solutions
Answer 265273 by mananth(12270) on 2010-11-17 01:19:55 (Show Source):
You can put this solution on YOUR website!plane travels 175 miles with the wind in the same amount of time it flew 150 miles against the wind. what was the speed of the plane in the still air if the wind was blowing at 20 mph?
..
let speed of plane in still air be x mph
wind speed = 20 mph
..
speed with wind = x+20: d=175 miles
against wind speed = x-20: d= 150 miles
...
175/(x+20)=150(x-20)
175(x-20)=150(x+20)
175x-3500=150x+3000
reorganise
25x=6500
/25
x=6500/25
x=260 mph speed of plane in still air
...
m.ananth@hotmail.ca
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Geometry_Word_Problems/372455: A 5 inch by 8 inch rectangular picture has a frame of uniform width. if the area of the frame is 114 square inches, what is the width of the frame?
1 solutions
Answer 265270 by mananth(12270) on 2010-11-17 01:05:10 (Show Source):
You can put this solution on YOUR website!Picture width = 5 in
picture length = 8 in
Area = 40 in^2
...
uniform width let it be x in
..
total width = 5+2x
total length = 8+2x
..
Total area = (5+2x)(8+2x)
=40+10x+16x+4x^2
=4x^2+26x+40
...
Total area - picture area = area of frame
4x^2+26x+40 -40=114
4x^2+26x-154=0
...
use the quadratic formula to get the roots of the equation
discriminant = 3140
x1= 
x1= 3.75
x2= 
x2=-10.25 ( ignore )
width = 3.75 in
..
m.ananth@hotmail.ca
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Travel_Word_Problems/372381: Nancy jogs and walks to school each day. She averages 4 Km/h walking and 8 Km/h jogging.The distance from home to school is 6 Km, and she makes the trip in 1hour.How far does she jog in a trip?
1 solutions
Answer 265248 by mananth(12270) on 2010-11-16 21:59:28 (Show Source):
You can put this solution on YOUR website!Nancy jogs and walks to school each day. She averages 4 Km/h walking and 8 Km/h jogging.The distance from home to school is 6 Km, and she makes the trip in 1hour.How far does she jog in a trip?
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walking 4km/h
jogging 8km/h
..
distance = 6 km to school
time taken = 1hour
..
jogging distance be x km
walking distance = 6-x
..
t = d/r
time jogging + time walking = 1
x/8 + x/4 = 1
(x+2x)/8 = 1
multiply by 8
3x = 8
/3
x= 8/3
x=2.66 km
...
m.ananth@hotmail.ca
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Surface-area/372370: The volume of a sphere of radius r is V = 4/3 pir^3
use the formula to find r in terms of V. Rationalize the denominator
1 solutions
Answer 265246 by mananth(12270) on 2010-11-16 21:45:41 (Show Source):
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Systems-of-equations/372373: How do you solve for y in the following equations:
-3/4x+y/3=5/12
x/5-y=4/5
1 solutions
Answer 265242 by mananth(12270) on 2010-11-16 21:39:29 (Show Source):
You can put this solution on YOUR website!(-3x/4)+y/3=5/12
(-9x+4y)/12= 5/12
multiply by 12
-9x+4y=5......................1
x/5-y=4/5
(x-5y)/5 = 4/5
multiply by 5
x-5y = 4......................2
..
multiply equation 2 by 9
9x-45y=36
add to (1)
-45y+4y=36+5
-41y=41
/-41
y =-1
..
plug value of y in 1
-9x-4=5
-9x= 4+5
/-9
x=-1
...
m.ananth@hotmail.ca
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Rate-of-work-word-problems/372353: I don't know how to set up the equation for this word problem...
My cat Archimedes can rid my garage of mice twice as fast as my neighbor's cat, Pythagoras. If they joined forces, they can clear a garage in a mere two hours. In how many hours does it take for each of these felines to clear a garage of mice working alone?
I think the known values are:
Pythagoras's rate = x
Archimedes' rate = 2x
Total time working together = 2 hours
Thank you!
1 solutions
Answer 265234 by mananth(12270) on 2010-11-16 21:20:51 (Show Source):
You can put this solution on YOUR website!Pythagoras's rate = x
Archimedes' rate = 2x
Total time working together = 2 hours
...
I will continue your steps
..
Pythagoras's can do 1/x of the job in 1 hour
Archimedes' can do 1/ 2x of the job in 1 hour.
...
together they can do 1/x + 1/2x of the job in 1 hour
(2+1)/2x
=2+1/2x
=3/2x
So they will take 2x/3 hours to do the job. = 2
2x/3=2
multiply by 3
2x = 6
/2
x=3 Pythagoras's time
2x= 6 hours = Archimedes
..
so you know how many hours they take
...
m.ananth@hotmail.ca
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