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15390..15419 , 15420..15449 , 15450..15479 , 15480..15509 , 15510..15539 , 15540..15569 , 15570..15599 , 15600..15629 , 15630..15659, >>NextTravel_Word_Problems/503002: John drove his car into the shop to fix the oil leak in his engine. Once finished, his car was faster. He drove home in only 25 minutes when it took him 40 minutes to get there. If he was traveling an average of 32 miles per hour going there, how fast did he drive home?
1 solutions
Answer 339163 by ankor@dixie-net.com(15656)   on 2011-09-23 20:12:02 (Show Source):
You can put this solution on YOUR website!John drove his car into the shop to fix the oil leak in his engine.
Once finished, his car was faster. He drove home in only 25 minutes when it took him 40 minutes to get there.
If he was traveling an average of 32 miles per hour going there, how fast did he drive home?
:
Change minutes to hours
 =  hrs
 =  hrs
:
Let s = his speed going home
:
The distance there and back are equal, write a dist equation; Dist = time * speed
:
s = (32)
mult both side by 12
5s = 8(32)
5s = 256
s = 
s = 51.2 mph return speed
:
:
Confirm this by finding the distances, they should be equal
*51.2 = 21.33 mi
*32 = 21.33 mi
|
Polynomials-and-rational-expressions/503159: using the steps to the foil method can you break down how to get the answer to this (4z-u)(6z+4u)?
1 solutions
Answer 339160 by ankor@dixie-net.com(15656) on 2011-09-23 19:57:15 (Show Source):
You can put this solution on YOUR website!(4z-u)(6z+4u)?
First: mult the first two terms: 4z*6z = 24z^2
Outer: mult the first & last terms: 4z*4u = 16zu
Inner: mult the inner terms: -u*6z = -6zu
Last: mult the last terms: -u*4u = -4u^2
:
Put them together
24z^2 + 16zu - 6zu - 4u^2
:
the middles are like terms combine them
24z^2 + 10zu - 4u^2
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Rational-functions/503204: Please help!! I have to show a table of values for -3x + 4y = -12.
I have no idea. I keep trying to show how to figure it out but I cant.
Thanks so much!!
1 solutions
Answer 339120 by ankor@dixie-net.com(15656) on 2011-09-23 16:47:51 (Show Source):
You can put this solution on YOUR website!show a table of values for -3x + 4y = -12.
Convert equation to the slope/intercept form
-3x + 4y = -12
4y = 3x - 12
divide by 4
y =  x - 3
:
We will construct a table using x values of -3 to + 3
Substitute -3 for x and find y
y = (-3) - 3
y =  - 3
y = - 
y = 
y = -5.25
do the same for x=-2, -1, 0, +1, +2, +3,
The table
x | y
-------
-3 |-5.25
-2 |
-1 |-3.75
0 |
+1 |-2.25
+2 |
+3 |-.75
:
You can fill in the missing y values
|
Miscellaneous_Word_Problems/502925: Read the problem. What are you being asked to find? What would be your let statement? Do you need to know any formulas to work this problem? If your answer is yes, then what formulas do you need to know? Would a chart help organize the information in this problem? If your answer is no, state why not and if your answer is yes, then make a chart that will organize the information.
If 92 is added to a number, the result is 44 less than three times the number. Find the number
1 solutions
Answer 339116 by ankor@dixie-net.com(15656) on 2011-09-23 16:31:36 (Show Source):
You can put this solution on YOUR website!If 92 is added to a number, the result is 44 less than three times the number.
Just write exactly what it says
92 + n = -44 + 3n
some basic algebra
92 + 44 = 3n - n
136 = 2n
n = 
n = 68
:
:
Check solution in original statement
92 + 68 = -44 +3(68)
160 = -44 + 204
160 = 160; OK
|
Word_Problems_With_Coins/502910: Maria has 20 coins in her pocket, all nickels and dimes. The total value of the coins is $1.35. How many of each type of coin does she have in her pocket?
PLEASE I NEED HELP ASAP
if you could help me show HOW you got to there that would be so helpful :)
THANK YOU!!!
1 solutions
Answer 339115 by ankor@dixie-net.com(15656) on 2011-09-23 16:27:05 (Show Source):
You can put this solution on YOUR website!Maria has 20 coins in her pocket, all nickels and dimes.
The total value of the coins is $1.35. How many of each type of coin does she have in her pocket?
:
let n = no. of nickels
let d = no. or dimes
;
Write an equation for each statement:
"Maria has 20 coins in her pocket, all nickels and dimes."
n + d = 20
n = (20-d), use this form for substitution
:
"The total value of the coins is $1.35."
.05n + .10d = 1.35
From the 1st statement, substitute n with (20-d)
.05(20-d) + .10d = 1.35
1 - .05d + .10d = 1.35
.05d = 1.35 - 1
.05d = .35
d = 
d = 7 dimes
:
You can find n, yourself, check that the total is 1.35
|
Miscellaneous_Word_Problems/503165: Urgent Response. Can a tutor be so kind to help with solving this problem?
AKI's Bicycle Shop designs has determined that when x hundred bicycles are built,the average cost per bicycle is given by C(x)=0.1x^2-11.2x+9.232 where
C(x) is in hundreds of dollars.
How many bicycles should the shop build? _____
1 solutions
Answer 339111 by ankor@dixie-net.com(15656) on 2011-09-23 15:57:19 (Show Source):
You can put this solution on YOUR website!AKI's Bicycle Shop designs has determined that when x hundred bicycles are built,
the average cost per bicycle is given by C(x)=0.1x^2-11.2x+9.232 where
C(x) is in hundreds of dollars.
How many bicycles should the shop build? _____
:
I assume they want to find the no. of bikes that will give minimum cost per bike
:
This is a quadratic equation where the minimum can be found by using the axis of symmetry formula: x = -b/(2a)
In this equation a = .1, b = -11.2
therefore
x =  = 
x = 56 hundred bikes for min cost per bike
|
Exponential-and-logarithmic-functions/502985: How to use exponentials to solve the following equation. (ii) 7+3e(to the power x)=3/e(to the power x+6) +7
1 solutions
Answer 339100 by ankor@dixie-net.com(15656) on 2011-09-23 14:59:15 (Show Source):
You can put this solution on YOUR website!How to use exponentials to solve the following equation. (ii)
7+3e(to the power x)=3/e(to the power x+6) +7
:
7 + 3  =  + 7
Subtract 7 from both sides
3 =
Change the sign of the exponent to give us the reciprocal
 =
when the numerators are equal, the denominators are equal, therefore:
 = 
therefore
-x = x + 6
-6 = x + x
-6 = 2x
x = -3
:
:
Check this in the original equation
7 + 3  =  + 7
Change the sign of the exponent to give us the reciprocal
7 +  =  + 7
|
Numbers_Word_Problems/502890: A two digit number is 3 times the sum of it's digits. The number is also 45 less than the number formed by reversing the digits and the original number. What is the original number?
1 solutions
Answer 338995 by ankor@dixie-net.com(15656) on 2011-09-22 21:55:45 (Show Source):
You can put this solution on YOUR website!Let x = the 10's digit, let y = the units
:
A two digit number is 3 times the sum of it's digits.
10x + y = 3(x+y)
10x + y = 3x + 3y
10x - 3x = 3y - y
7x = 2y
:
The number is also 45 less than the number formed by reversing the digits and the original number.
10x + y = 10y - x - 45
10x - x = 10y - y - 45
9x = 9y - 45
simplify, divide by 9
x = y - 5
:
In the 1st simplified equation replace x with (y-5)
7(y-5) = 2y
7y - 35 = 2y
7y - 2y = 35
5y = 35
y = 35/5
y = 7 is the units digit (original number)
and
x = 7 - 5
x = 2 is the 10's digit
:
27 is the number
:
:
Check it in the statement:
"A two digit number is 3 times the sum of it's digits.
27 = 3(7+2)
|
expressions/502765: Using the pemdas formula, I need to put 6, 6, 6, and 6 to equal 6. I am having difficulty trying to come up with the sum of 6. Please help.
1 solutions
Answer 338985 by ankor@dixie-net.com(15656) on 2011-09-22 21:40:21 (Show Source):
You can put this solution on YOUR website!Using the pemdas formula, I need to put 6, 6, 6, and 6 to equal 6. I am having difficulty trying to come up with the sum of 6.
:
How about 6(6-6)+6 = 6?
|
Miscellaneous_Word_Problems/502757: Joey and Sally are on a hiking trip. It will be dark in 1.5 hours. They have to decide whether to stop for the night or hike to the camp site at the base of a tower they can see in distance. They know the height of the tower is 315 metres and they use a clinometer to determine the angle of elevation to the top of the tower is 4.
Joey and Sally have been walking at 3.5 km/hr . Should they stop for the night or continue walking?
1 solutions
Answer 338979 by ankor@dixie-net.com(15656) on 2011-09-22 21:30:00 (Show Source):
You can put this solution on YOUR website!Joey and Sally are on a hiking trip. It will be dark in 1.5 hours.
They have to decide whether to stop for the night or hike to the camp site at the base of a tower they can see in distance.
They know the height of the tower is 315 metres and they use a clinometer to determine the angle of elevation to the top of the tower is 4.
:
Use the tangent of 4 degrees to find the distance (d) to the tower (side adjacent) and side opposite = 315
tan(4) = 
d = 
d = 4507.71 meters ~ 4.5 km to the base of the tower
:
Joey and Sally have been walking at 3.5 km/hr .
Should they stop for the night or continue walking?
:
they are about 4.5 km from the tower, find the time to walk this dist at 3.5 km/hr
 = 1.287 hrs, they should make it with about 13 min to spare
|
test/502789: Angela is driving a Ferrari along the interstate at a constant speed of 55mph. A Volkswagon one-half mile behind her that is moving at a constant speed passed her in 90 seconds. How many miles per hour is the speed of the Volkswagon?
1 solutions
Answer 338970 by ankor@dixie-net.com(15656) on 2011-09-22 21:11:36 (Show Source):
You can put this solution on YOUR website!Angela is driving a Ferrari along the interstate at a constant speed of 55mph.
A Volkswagon one-half mile behind her that is moving at a constant speed passed her in 90 seconds. How many miles per hour is the speed of the Volkswagon?:
:
Let v = the Volkswagon speed
:
Change 90 sec to hrs: 90/3600 = .025 hrs
:
Write a time equation: time = dist/speed
:
 = .025 hrs
.5 = .025(v-55)
.5 = .025v - 1.375
.5 + 1.375 = .025v
1.875 = .025v
v = 
v = 75 mph is the Volkswagon
|
Travel_Word_Problems/502461: Linda drove from Phila. to NYC at the rate of 50 mph. She made the trip from NYC to Phila., along the same route, traveling at 40 mph. Her total driving time was 3.6 hours. Find the distance between Phila. and NYC.
1 solutions
Answer 338885 by ankor@dixie-net.com(15656) on 2011-09-22 15:35:30 (Show Source):
You can put this solution on YOUR website!Linda drove from Phila. to NYC at the rate of 50 mph.
She made the trip from NYC to Phila., along the same route, traveling at 40 mph.
Her total driving time was 3.6 hours.
Find the distance between Phila. and NYC.
:
Let d = dist from Philly to NY
Write a time equation, time = dist/speed
:
To time + return time = 3.6 hrs
 +  = 3.6
multiply by 200 to clear the denominators, results
4d + 5d = 200(3.6)
9d = 720
d = 720/9
d = 80 mi
;
:
Check this by finding the actual time of each trip
80/50 = 1.6 hrs
80/40 = 2.0 hrs
-----------------
total: 3.6 hrs
|
Travel_Word_Problems/502437: I need help on the word problem. Alex and Betty walk at 4 mph to their car. It takes them almost an hour. In their car, they travel (at 16 mph) the same distance as they walked. All together, their walking and traveling by car took exactly one hour. How long did they walk?
1 solutions
Answer 338881 by ankor@dixie-net.com(15656) on 2011-09-22 15:01:44 (Show Source):
You can put this solution on YOUR website!Alex and Betty walk at 4 mph to their car. It takes them almost an hour.
In their car, they travel (at 16 mph) the same distance as they walked.
All together, their walking and traveling by car took exactly one hour.
How long did they walk?
:
Let t = time spent walking (in hrs)
then it said the round trip took 1 hr therefore:
(1-t) = time spent driving
:
The walking dist and the driving dist is the same, write a dist equation: dist = speed * time
:
walk dist = drive dist
4t = 16(1-t)
4t = 16 - 16t
4t + 16t = 16
20t = 16
t = 
t = .8 hrs walking
:
:
:
Check this (.2 hrs driving)
4(.8) = 3.2 mi
16(.2)= 3.2 mi; confirms our solution of .8 hrs spend walking
|
Surface-area/502413: how can I know how many gallions of paints to cover my living room that measures 30ft by 18ft?
1 solutions
Answer 338878 by ankor@dixie-net.com(15656) on 2011-09-22 14:52:54 (Show Source):
You can put this solution on YOUR website!how can I know how many gallons of paints to cover my living room that measures 30ft by 18ft?
:
Find the area of the painted area. If you are covering all 4 walls and the ceiling is 8 ft high:
2(30*8) + 2(18*8) =
2(240) + 2(144) = 768 sq/ft,
if you include the ceiling, add another 30*18 = 540 sq/ft
:
Of course it will probably be a little less because of doors and windows, but this will give you a good idea
:
Paint cans tell you how many sq ft it will cover, usually around 450 sq/ft
Divide the total area you are going to paint by that amt, round it up to the nearest gallon.
:
If you are changing the color drastically you may need to paint it twice.
|
Proportions/502322: a masons can build a 12 meters long wall in 4 days. find how many masons are required to build the 27 meters long wall in 3 days?
1 solutions
Answer 338877 by ankor@dixie-net.com(15656) on 2011-09-22 14:32:20 (Show Source):
You can put this solution on YOUR website! a masons can build a 12 meters long wall in 4 days.
:
The number of man-days per meter requires:  =  man-days per meter
:
:
find how many masons are required to build the 27 meters long wall in 3 days?
:
A 27 meter wall requires
27 * =  = 9a man-days
m = no. of masons required
3m = 9a
Divide by3
m = 3a
3a masons required to accomplish this
|
percentage/502227: I am having problems with this word problem:
Raul paid a total of $26.40 for a meal. This total included a 20% tip. How much was the cost of the meal?
1 solutions
Answer 338788 by ankor@dixie-net.com(15656) on 2011-09-21 21:55:36 (Show Source):
You can put this solution on YOUR website!Raul paid a total of $26.40 for a meal.
This total included a 20% tip.
How much was the cost of the meal?
:
Let m = cost of the meal
:
Meal + tax = 26.40
m + .20m = 26.40
1.2m = 26.40
m = 
m = $22 for the meal
:
:
Check this
meal alone cost = 22
tip cost: .2(22) = 4.40
--------------------------
total, meal & tip 26.40
|
Rate-of-work-word-problems/501622: if 24 adult can finish a work in 16 days and 16 children can finish the same work in 48 days then how much time it would take one adult and 1 child to finish the work?
1 solutions
Answer 338722 by ankor@dixie-net.com(15656) on 2011-09-21 16:38:47 (Show Source):
You can put this solution on YOUR website!if 24 adult can finish a work in 16 days and 16 children can finish the same work in 48 days then how much time it would take one adult and 1 child to finish the work?
:
We know it takes
24*16 = 384 man-days to do the job
or
16*48 = 768 child-days (twice as many as man-days)
Therefore:
2 child-days = 1 man-day
:
"then how much time it would take one adult and 1 child to finish the work?
let d = no. of days for 1 child and 1 man to do the job
:
1 child and 1 man = 1.5 man
:
1.5d = 384
d = 
d = 256 days for one man and one child to do the job
:
:
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Miscellaneous_Word_Problems/501599: write equation
Mrs. Beal. a retiree will lose some retirement benefits if she earns over $8000 per year working at baby sister.if she has already earned $6500, for how many more hours may she work at $7.50 per hour without losing her retirement benefits?
1 solutions
Answer 338711 by ankor@dixie-net.com(15656) on 2011-09-21 16:21:15 (Show Source):
You can put this solution on YOUR website!Mrs. Beal. a retiree will lose some retirement benefits if she earns over $8000 per year working at baby sister.if she has already earned $6500,
for how many more hours may she work at $7.50 per hour without losing her retirement benefits?
:
h =  = 200 hrs
:
:
Check this
200(7.50) + 6500 = 8000
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Linear-systems/501602: Solve the following system (if possible) and place your answer below:
3/x - 2/y = -30
2/x - 3/y = -30
1 solutions
Answer 338707 by ankor@dixie-net.com(15656) on 2011-09-21 16:07:31 (Show Source):
You can put this solution on YOUR website!
:
Multiply the 1st equation by 2, the 2nd equation by 3:
-------------subtraction eliminates x, find y
+ 
30y = 5
y = 
y = 
:
Find x using the 1st equation
 - 
= -30 + 12
= -18
-18x = 3
x = 
x = 
:
:
Check solutions in the 2nd equation
 - 
-12 - 18 = -30
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Reduction-of-unit-multipliers/501723: In a downhill ski race, Margo posted a time of 2 minutes and 24 seconds for a course 2.1 miles long. How many miles per hour did she average for the race?
1 solutions
Answer 338703 by ankor@dixie-net.com(15656) on 2011-09-21 15:47:38 (Show Source):
You can put this solution on YOUR website!In a downhill ski race, Margo posted a time of 2 minutes and 24 seconds for a course 2.1 miles long. How many miles per hour ?
:
Change 2 min 24 sec to 144 sec
:
 = 68.57 sec/mi
:
Convert to mph (3600 sec in 1 hr)
 = 52.5 mph
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Money_Word_Problems/501722: when you use your car for business you are able to deduct expenses on your income tax. Milage rates are 55.5 cents per mile. How many miles did the tax-payer drive who deducted &8880.00.
1 solutions
Answer 338701 by ankor@dixie-net.com(15656) on 2011-09-21 15:32:58 (Show Source):
You can put this solution on YOUR website!when you use your car for business you are able to deduct expenses on your income tax. Milage rates are 55.5 cents per mile.
How many miles did the tax-payer drive who deducted &8880.00.
:
 = 16,000 miles, that's pretty easy, isn't it?
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Miscellaneous_Word_Problems/501561: The height of an object tossed upward with an initial velocity of 104 feet per second is given by the formula h = -16t^2 + 104t, where h is the height in feet and t is the same time in seconds. Find the time required for the object to return to its point of departure.
Please, I need this problem to be solved by tomorrow night (9/21/2011). Thanks.
1 solutions
Answer 338700 by ankor@dixie-net.com(15656) on 2011-09-21 15:29:17 (Show Source):
You can put this solution on YOUR website!The height of an object tossed upward with an initial velocity of 104 feet per second is given by the formula h = -16t^2 + 104t, where h is the height in feet and t is the same time in seconds.
Find the time required for the object to return to its point of departure.
:
the point of departure (ground level) h = 0, therefore
-16t^2 + 104t = 0
Factor out -16t, results
-16t(t - 6.5) = 0
Two solutions
t = 0 sec, when object is tossed, it as at ground level
and
t = 6.5 sec, when object returns to earth
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Travel_Word_Problems/501784: Maria paints portraits that she sells for $30 each. Her cost, C, is C= 160+16n, where n = number of portraits sold. Write an inequality to represent the number of portraits she needs to sell to earn a profit of at least $300
1 solutions
Answer 338696 by ankor@dixie-net.com(15656) on 2011-09-21 15:17:29 (Show Source):
You can put this solution on YOUR website!Maria paints portraits that she sells for $30 each.
Her cost, C, is C= 160+16n, where n = number of portraits sold.
Write an inequality to represent the number of portraits she needs to sell to earn a profit of at least $300
:
Revenue; r = 30n
cost; c = 160 + 16n
r - c = profit; therefore
:
30n - (160+16n) => 300
30n - 160 - 16n => 300
30n - 16n = 300 + 160
14n => 460
n => 
n => 33 portraits to make at least $300
:
:
:
Check this
30(33) = $990 revenue
160 + 16(33) = $688 cost
-----------------------
profit: $302
:
You can check this with 32 portraits and see it will be less than $300 profit
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Travel_Word_Problems/501761: The Fortune Family leaves home at 6:00 AM to go on vacation. They travel 50 miles per hour. Their next door neighbor, the Bissets leave home at 8:00 AM to go on vacation. They travel at 60 miles per hour. If the Fortunes and Bissets are traveling the same route to the same location, after how many hours will the Bissets be 40 miles ahead of the Fortunes?
I am having the hardest time with this problem! I am not even sure how to begin to set it up, let alone solve it.
1 solutions
Answer 338684 by ankor@dixie-net.com(15656) on 2011-09-21 14:43:09 (Show Source):
You can put this solution on YOUR website!The Fortune Family leaves home at 6:00 AM to go on vacation.
They travel 50 miles per hour.
Their next door neighbor, the Bissets leave home at 8:00 AM to go on vacation.
They travel at 60 miles per hour.
If the Fortunes and Bissets are traveling the same route to the same location, after how many hours will the Bissets be 40 miles ahead of the Fortunes?
:
Let t = travel time of the Bissets
The Fortune family leaves two hr earlier, therefore
(t+2) = travel time of Fortunes
:
Write a distance equation, dist = speed * time
:
B's dist - F's dist = 40 mi
60t - 50(t+2) = 40
60t - 50t - 100 = 40
10t = 40 + 100
10t = 140
t = 
t = 14 hrs for the B's to be 40 mi ahead of the F's
;
:
We can confirm this by finding the actual dist each drove in 14 & 16 hrs
60*14 = 840 mi
50*16 = 800 mi
---------------
differ: 40 mi
:
:
Hey don't sound so discouraged, did this make sense to you? Develop a thought pattern that translates each phrase to a simple expression or equation.
Then use the dist, time, speed relationships that I am sure you know. Let me know what you think, please. C
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Travel_Word_Problems/501780: Hi,
My daughter who is in sixth grade got this question:
A lorry travels from Town A to Town B in 4 & 1/5 hrs. A car travels from Town B to Town A in 3 hrs. If both started at the same time, after how long did they pass across each other? She is not allowed to use formulas and equations involving x, y etc. Can you please explain how to solve this without using equations?
Thanks.
1 solutions
Answer 338662 by ankor@dixie-net.com(15656) on 2011-09-21 13:51:26 (Show Source):
You can put this solution on YOUR website!A lorry travels from Town A to Town B in 4 & 1/5 hrs.
A car travels from Town B to Town A in 3 hrs.
If both started at the same time, after how long did they pass across each other?
:
I can't see how you can solve this without some equations, and why would you not want to? I assume we can use numbers and rules that govern there relationships.
Anyway, there is mathematical relationship between these values which is used in electronics, called the "product over sum" relationship
:
 =  = 1.75 hrs travel time when they met
:
:
:
I admit I used algebra equations to confirm that this is right, in case you're interested.
Choose a value for the distance between the towns, I chose 21 mi a multiple of 4.2 and 3
Found the speed: 21/4.2 = 5 mph and 21/3 = 7 mph, let t = time for them to meet
5t + 7t = 21
12t = 21
t = 
t = 1.75 hrs
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