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Inequalities/350042: please help me in this problem set! An organization wants to sell tickets to a concert. it plans on selling 300 reserved-seat tickets and 150 tickets at the door. the price of a reserved-seat ticket is to be $2 more than a ticket at the door. if the organization wants to collect at least $3,750, what is the maximum it can charge for a reserved-seat ticket?
1 solutions
Answer 250179 by mananth(12270)   on 2010-09-30 01:30:32 (Show Source):
You can put this solution on YOUR website!300 reserved-seat tickets
150 tickets at the door.
..
ticket at door be x
price of a reserved-seat ticket is to be $2 more = x+2
collection $3,750,
...
150x+300(x+2)=3750
150x+300x+600=3750
450x=3750-600
450x=3150
x=$ 70 at the door price
reserved = $ 72
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Travel_Word_Problems/350028: The speed of the freight train is 23 mph slower than that of a passenger train. The freight train travels 250 miles in the same time it takes the passenger train to travel 450 miles. Find the speed of the passenger train.
1 solutions
Answer 250172 by mananth(12270) on 2010-09-30 00:33:12 (Show Source):
You can put this solution on YOUR website!freight train speed = x mph
passenger train speed = x+23 mph
..
distance by freight train = 250 miles
distrance by passenger = 450 miles.
..
Time taken by both = same
..
250/x = 450/(x+23)
250(x+23)=450x
250x+5750=450x
450x-250x=5750
200x = 5750
/200
x= 5750/200
x=28.75 mph freight train
passenger train speed = 28.75+23=51.75mph
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Proportions/350020: If Soc can paint 100 easter eggs in 165 minutes and Ngu can paint 100 easter eggs in 205 minutes and Fawn can paint 100 easter eggs in 120 minutes how long will it take for the three of them working together to paint 100 easter eggs ?
1 solutions
Answer 250166 by mananth(12270) on 2010-09-30 00:15:56 (Show Source):
You can put this solution on YOUR website! Soc can paint 100 easter eggs in 165 minutes
1/165 of the job he does in 1 minute
Ngu can paint 100 easter eggs in 205 minutes
1/205 of the job in 1 minute
Fawn can paint 100 easter eggs in 120 minutes
1/120 of the job in 1 minute
...
Together they will do 1/165 + 1/205 + 1/120 of the job in 1 minute
0.019 of the job in 1 minute.
..
so for total job they will take 1/0.019 minutes
51.88 minutes
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Geometric_formulas/349983: the perimeter of a college basketball court is 96m and the lenght is 14m more than the width. what are the dimensions.
1 solutions
Answer 250165 by mananth(12270) on 2010-09-30 00:07:25 (Show Source):
You can put this solution on YOUR website!let width =x
length = x+14
..
Perimeter = 96 = 2*(L+W)
96=2*(X+X+14)
96=2*(2x+14)
96=4x+28
96-28=4x
68=4x
/4
68/4=x
17=x the width
length = 17+14= 31m
...
CHECK
17+17+31+31=96
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Angles/350011: the measure of one of two supplementary angles is 4 greater than 3 times the other. Find the measure of the larger angle
1 solutions
Answer 250162 by mananth(12270) on 2010-09-30 00:00:14 (Show Source):
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Mixture_Word_Problems/349990: The Denver Chemical Company wants to increase its 10% peroxide solution to a 28% solution by adding 100% peroxide. If Denver has 500 gallons its original 10% peroxide, how much pure peroxide must it add to obtain the new mixture?
1 solutions
Answer 250161 by mananth(12270) on 2010-09-29 23:55:23 (Show Source):
You can put this solution on YOUR website!10% peroxide solution 500 gallons
100% let it be x gallons
to a 28% solution total = 500 +x gallons
..
0.1*500 +x = 0.28(500+x)
50+x =140+0.28x
x-0.28x=140-50
0.72x=90
/0.72
x=90/0.72
125 gallons
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Rate-of-work-word-problems/350001: If bob can mow a lawn in 5 hours, and jim can mow the same lawn in 3 hours,how long will it take if they work together?
1 solutions
Answer 250157 by mananth(12270) on 2010-09-29 23:39:04 (Show Source):
You can put this solution on YOUR website!Bob can do the job in 5 hours
so he does 1/5 of the job in 1 hour.
..
Jim does in 3 hours.
he does 1/3 of the job in 1 hour.
Together they do 1/3 + 1/5 of the job in 1 hour
=8/15 of the job.
so they will take 15/8 hours to do the job together.
1.87 hours
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Proportions/350002: The ratio of male students to female students at a certain university is 5 to 4. If there is a total of 6975 students, find the number of male students and the number of female students.
1 solutions
Answer 250153 by mananth(12270) on 2010-09-29 23:35:34 (Show Source):
You can put this solution on YOUR website!male to female = 5/4
total students = 6975
..
total parts = 5+4 = 9
...
Male students = 5/9 * 6975 = 3875
female = 4/9 * 6975 = 3100
...
CHECK
3875 + 3100 = 6975
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Age_Word_Problems/349994: Zelma is eighteen years older than her son. She was three times as oldas he was one year ago. How old are they now?
1 solutions
Answer 250149 by mananth(12270) on 2010-09-29 23:26:54 (Show Source):
You can put this solution on YOUR website!let son be x years
Zelma = x+18
..
1 year ago
son was x-1 years
Zelma was x+18-1 = x+17 years
..
x+17 = 3(x-1)
x+17 = 3x-3
3x-x =17+3
2x=20
/2
x=10 son's age
Zelma = 10 + 18 = 28 years.
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Geometry_Word_Problems/349989: A landscaper, who just completed a rectangular flower garden measuring 6 feet by 10 feet, orders 1 cubic yard of premixed cement, all of which is to be used to create a border of uniform width around the garden. If the border is to have a depth of 3 inches, how wide will the border be?
1 solutions
Answer 250148 by mananth(12270) on 2010-09-29 23:21:57 (Show Source):
You can put this solution on YOUR website!garden = 6ft by 10ft. Area of garden = 60 sq. ft.
1 cu. yard = 3*3*3 = 27 cu.ft
..
The volume of concrete border = 27cu.ft.
the thickness = 3 inches. = 3/12 ft = 1/4 ft.
...
volume of concrete = L*W*H
L*W= volume / height
volume = 27cu.ft
height or thickness = 3in.
Area of the border = 27/(1/4 )
L*W= 27*4/1 = 108 sq. inches.
..
area of garden + area of border = 60+108 = 168 sq.ft
let width of border be x feet. increase in length & width =2x
(6+2x)(10+2x)= 168 sq. ft
60+12x+20x+4x^2=168
4x^2+32x+60-168 =0
4x^2+32x-108=0
/4
x^2+8x-27 =0
solve by quadratic formula you get x = 2.56 feet.
The width will be 2.56 feet
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Proportions/349987: A saltwater solution is made by dissolving 3 pounds of salt in 10 gallons of water. At this rate, how many pounds of salt are needed for 25 gallons of water.
1 solutions
Answer 250145 by mananth(12270) on 2010-09-29 22:58:27 (Show Source):
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Geometry_Word_Problems/349986: A homeowner is covering his patio with carpet squares, the area of the patio is 100 feet square, if each carpet square measures 8 inches by 8 inches, how many squares will it take to cover the patio?
1 solutions
Answer 250144 by mananth(12270) on 2010-09-29 22:56:25 (Show Source):
You can put this solution on YOUR website!Area of patio = 100 sq.ft
square carper is 8 by 8 inches
..
since area of patio is in sq. ft. convert the length of carpet to feet.
8" = 8/12 feet
=3/4 ft.
area of carpet = 3/4 * 3/4 = 9/16 sq.ft.
number of carpet squares = area of aptio/area of carpet squares
100 / (9/16)
100*16/9
=1600/9
=225 squares
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Radicals/349918: The hypotenuse of an isosceles right triangle is 16 centimeters. Find the length of the two other sides of the triangle to the nearest tenth.
1 solutions
Answer 250094 by mananth(12270) on 2010-09-29 21:15:35 (Show Source):
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Geometry_Word_Problems/349920: If you cut out the largest possible circular pie crust for a square piece of dough that is "d" inches on a side, what is the area of the remaining dough? Express your answer as polynomial in "d".
1 solutions
Answer 250093 by mananth(12270) on 2010-09-29 21:11:04 (Show Source):
You can put this solution on YOUR website!area of square piece = d*d= d^2
...
area of circle = pi*r^2 where r= radius.
....
diameter = d
radius = d/2
area = pi(d/2 )^2
area = pi*d^2/4
..
remaining area = area of square - arae of circle
d^2- pi*d^2/4
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Mixture_Word_Problems/349919: Roger's age is 1 1/3 times Steven's age. Eight years ago, Roger's age was twice Steven's age. Find Roger's age.
1 solutions
Answer 250090 by mananth(12270) on 2010-09-29 21:05:06 (Show Source):
You can put this solution on YOUR website!let steven's age be x
roger's age = 1 1/3 times stevens age.
=4/3 times = 4x/3
...
8 years ago
steven's age = x-8
roger's age = 4x/3 - 8
...
4x/3 -8 = 2(x-8)
(4x-24)/3 = 2x-16
x3
4x-24=3(2x-16)
4x-24=6x-48
6x-4x=48-24
2x=24
x=12 steven's age
Roger = 4/3 * 12
=16 years
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Miscellaneous_Word_Problems/349928: At the park, I saw boys and dogs. I saw thirty two heads and 104 legs. How many were dogs and how many boys? Which equations did you use? I got 12 boys and 20 dogs by trial and error but I know that there must be some equations to solve. Please help. Thank you.
1 solutions
Answer 250087 by mananth(12270) on 2010-09-29 20:54:22 (Show Source):
You can put this solution on YOUR website!total 104 legs
32 heads
..
let there be x boys & y dogs
..
2x+4y=104..................1
x+y=32......................2
multiply equation 2 by -2 and add it to equation 1
-2x-2y=-64
add
4y-2y=104-64
2y=40
y=20 dogs
32-20= 12 boys
...
12*2+20*4=104
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Quadratic_Equations/349560: The area of a rectangular banner should be 6.75m^2. If the length is to be thrice the width, what are its dimensions? (Show your solution)
1 solutions
Answer 249845 by mananth(12270) on 2010-09-29 06:42:29 (Show Source):
You can put this solution on YOUR website!let width be x
length = 3x
..
Area = L*W
area = x*3x
3x^2 = 6.75 m^2
/3
x^2= 6.75/3
x^2= 2.25
x= 1.5 m the width
...
Length = 3x
3* 1.5 = 4.5 m
Check
1.5*4.5= 6.75 sq.m
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Surface-area/349561: the length of a rectangle is 7 more than the width. the area is 330 square centimeters. find the length and the width of the rectangle.
1 solutions
Answer 249843 by mananth(12270) on 2010-09-29 06:33:55 (Show Source):
You can put this solution on YOUR website!let width be x
length =x+7
..
Area = L*W
x(x+7)=330
x^2+7x=330
x^2+7x-330=0
x^2+22x-15x-330=0
x(x+22)-15(x+22)=0
(x+22)(x-15)=0
x= 15 is the width.
length = x+7 = 22
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Numbers_Word_Problems/349562: One number is 800 less than three times the other, and their sum is 1200. Find the numbers.
Please show me the solutions. As simplify as it can be...
1 solutions
Answer 249842 by mananth(12270) on 2010-09-29 06:30:01 (Show Source):
You can put this solution on YOUR website!let one number be x
the other number will be 1200-x. ( Because the sum of both is 1200)
..
one number is 800 less than the 3 times the other.
The other number is 1200-x
3 times other = 3(1200-x)
less 800
= 3(1200-x) -800
x=3(1200-x)-800
x=3600-3x-800
x+3x= 2400
4x = 2400
divide by 4
x= 2400/4
x=600
if one number is 600, then other is 1200-x=600.
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Circles/349563: pq and rs are two parallel horizontal chords 6 cm and 8 cm long in the upper half of a circle.if the radius of the circle is 5cm . the distance in cm between the chords is
A 1 B 2 C 3 D 4
1 solutions
Answer 249840 by mananth(12270) on 2010-09-29 06:23:47 (Show Source):
You can put this solution on YOUR website!The radius bisects the chord. The chords are of length 8 & 6.
The radius,perpendicular distance from center to chord and the chord form a right triangle.
Apply pythagorean formula
for both triangles
Radius is the hypotenuse.
5^2-4^2
25-16=9
sqrt9 = 3
....
5^2-3^2
25-9=16
sqrt16=4
the distance between the chords = 1 in.
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Linear_Equations_And_Systems_Word_Problems/349540: A student walks and jogs to school every day. She averages 4km/hour walking and 8km/hour jogging. The distance from home to school is 6km and the trip takes one hour. How far does the student walk.
1 solutions
Answer 249825 by mananth(12270) on 2010-09-29 00:58:09 (Show Source):
You can put this solution on YOUR website!walk = 4kph
jog 8 kph
..
distance to school = 6 km.
let her walk x km
she will jog 6-x km
..
Time walking = x/4
Time jogging = 6-x / 8
...
Total time = 1 hour
x/4 + (6-x)/8 =1
LCD = 8
(2x+6-x) / 8 =1
x+6 = 8
x= 2 km walking distance
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Distributive-associative-commutative-properties/349541: If a person is walking 6 miles per hour and another is riding a bike 12 MPH how far apart will they be after 10 minutes. Assuming they start next to each other and head in opposite directions.
Having trouble writing the equation.
1 solutions
Answer 249824 by mananth(12270) on 2010-09-29 00:47:48 (Show Source):
You can put this solution on YOUR website!walk speed = 6mph
cycling = 12mph
they are going in opposite directions
so effective speed = 12+6 = 18 mph.
time = 10 minutes
= 10/60 = 1/6 hour
..
Distance = speed * time
Distance = 18*1/6
= 3 miles apart
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Numbers_Word_Problems/349536: One number is one more than twice another number. The sum of the two squares of the two numbers is 97. I need to find the numbers... can you help?
1 solutions
Answer 249822 by mananth(12270) on 2010-09-28 23:46:54 (Show Source):
You can put this solution on YOUR website!LET ONENUMBER BE X
THE OTHER NUMBER = 2X+1
...
x^2+(2x+1)^2=97
x^2+4x^2+4x+1=97
5x^2+4x-96=0
5x^2+4x-96=0
5x^2-20x +24x-96=0
5x(x-4)+24(x-4)=0
(x-4)(5x+24)=0
x=4 OR -24/5
...
4 &9
-4.8, -8.6
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