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15390..15419 , 15420..15449 , 15450..15479 , 15480..15509 , 15510..15539 , 15540..15569 , 15570..15599 , 15600..15629, >>NextMiscellaneous_Word_Problems/161212: toms uncle owns a triangular piece of land. the perimeter fence that surrounds the land measures 378 yards. the shortest side is 30 yards longer than one-half of the longest side. the second longest side is 2 yards shorter than the longest side. what is the length of each side?
1 solutions
Answer 118753 by ankor@dixie-net.com(15638)   on 2008-10-09 16:17:47 (Show Source):
You can put this solution on YOUR website!the fence measures 378 yards. the shortest side is 30 yards longer than one-half of the longest side. the second longest side is 2 yards shorter than the longest side. what is the length of each side?
:
Let x = the longest side
:
from the statements,
"the shortest side is 30 yards longer than one-half of the longest side."
we can say:
.5x + 30 = the shortest side
and
" the second longest side is 2 yards shorter than the longest side."
x-2 = 2nd longest side
;
what is the length of each side?
:
Solve for x:
x + (.5x+30) + (x-2) = 378
x + .5x + x + 30 - 2 = 378
2.5x + 28 = 378
2.5x = 378 - 28
2.5x = 350
x = 
x = 140 yds is the longest side
then
.5(140) + 30 = 100 yd is the shortest side
and
140 - 2 = 138 yds is the 2nd side
:
:
Check: 140 + 100 + 138 = 378
|
Numbers_Word_Problems/161194: a girl buys three apples and seven oranges for $4.56. if an orange costs $0.28 more than an apple, how much does each fruit cost?
1 solutions
Answer 118750 by ankor@dixie-net.com(15638) on 2008-10-09 15:53:21 (Show Source):
You can put this solution on YOUR website!a girl buys three apples and seven oranges for $4.56. if an orange costs $0.28 more than an apple, how much does each fruit cost?
:
Let x = cost for an apple
Then
(x+.28) = cost for an orange (given information)
:
Write an equation for the statement:
"girl buys three apples and seven oranges for $4.56."
3x + 7(x+.28) = 4.56
:
3x + 7x + 1.96 = 4.56
:
3x + 7x = 4.56 - 196
:
10x = 2.60
:
x = 
x = .26 is the cost for an apple
then
.26 + .28 = .54 cost for an orange
:
:
Check solution in original equation:
3(.26) + 7(.54) =
.78 + 3.78 = 4.56
|
Rate-of-work-word-problems/161172: The radiator of a car holds 16 quarts of liquid of which 8 are antifreeze. The radiator has a leak and loses 2 quarts of liquid each week. Every week, 2 quarts of water are added. After 3 weeks how much antifreeze is left in the radiator? (explain your reasoning, just the answer is not sufficient).
1 solutions
Answer 118747 by ankor@dixie-net.com(15638) on 2008-10-09 15:36:28 (Show Source):
You can put this solution on YOUR website!The radiator of a car holds 16 quarts of liquid of which 8 are antifreeze. The radiator has a leak and loses 2 quarts of liquid each week. Every week, 2 quarts of water are added. After 3 weeks how much antifreeze is left in the radiator?
:
Let x = fractional amt of antifreeze after 2 qts leak out & 2 qt water added
:
Week 1:
 (16-2) = 16x (2 qts of water added to make it 16 again)
(14) = 16x
7 = 16x
x =  ;
Therefore: *16 = 7 qts, of antifreeze after week 1
:
Week 2;
(16-2) = 16x
14 = 16x
 = 16x
x = * 
x =  ;
Therefore: *16 = 6.125 qts of antifreeze after week 2
:
Week 3:
(16-2) = 16x
(14) = 16x
 = 16x
x = *
x =  ;
therefore: *16 = 5.34 qts of antifreeze after week 3
:
:
Hope this makes sense.
|
Miscellaneous_Word_Problems/161117: A 24-hour digital clock displays the hours and minutes throughout the course of a day. Such times as 2:42 and 13:31 are palindromic. What is the longest time lapse between successive palindromic times?
Please help me, kind tutor, I am in desperate need of your help.
Thank you so much!
1 solutions
Answer 118733 by ankor@dixie-net.com(15638) on 2008-10-09 12:23:06 (Show Source):
You can put this solution on YOUR website! 24-hour digital clock displays the hours and minutes throughout the course of a day. Such times as 2:42 and 13:31 are palindromic. What is the longest time lapse between successive palindromic times?
:
No one seems to want to do this, here is my effort, not positive about it,
but perhaps it will get you thinking in the right direction
:
Note that digits 6,7,8,9 do not occur in the minute's 10's digit position
:
From 1:01 to 1:51 every 10 min
From 1:51 to 2:02 = 11 min
From 2:02 to 2:52 every 10 min
From 2:52 to 3:03 = 11 min
From 3:03 to 3:53 every 10 min
From 3:53 to 4:04 = 11 min
Same until you get to: 9:59:
From 9:59 to 1001 = 2 min
From 1001 to 1111 = 1 hr 10 min
From 1111 to 1221 = 1 hr 10 min
same until you get 1551:
1551 to 2002 4 hrs 11 min, this is the longest time
2002 to 2112 1 hr 10 min
2112 to 2222 1 hr 10 min
2222 to 2332 1 hr 10 min
2332 to 1:01 1 hr 29 min
|
Quadratic_Equations/161020: Extreme hardship. Kim starts to walk 3 mi to school at 7:30 A.M. with a temperature of 0°F. Her brother Bryan starts at 7:45 A.M. on his bicycle, traveling 10 mph faster than Kim. If they get to school at the same time, then how fast is each one traveling?
1 solutions
Answer 118666 by ankor@dixie-net.com(15638) on 2008-10-08 20:09:44 (Show Source):
You can put this solution on YOUR website!Kim starts to walk 3 mi to school at 7:30 A.M. with a temperature of 0°F. Her brother Bryan starts at 7:45 A.M. on his bicycle, traveling 10 mph faster than Kim. If they get to school at the same time, then how fast is each one traveling?
:
Change 15 min to hrs: 15/60 = .25 hrs
:
Let s = K's walking speed
then
(s+10) = B's biking speed
:
Write a time equation: Time = 
:
K's travel time = B's travel time + .25 hr
 =  + .25
:
Multiply equation by t(t+10) to get rid of the denominator, results
3(s+10) = 3s + .25(s(s+10)
:
3s + 30 = 3s + .25s^2 + 2.5s
Arrange as a quadratic equation on the right
0 = .25s^2 + 2.5s + 3s - 3s - 30
:
.25s^2 + 2.5s - 30 = 0
Get rid of those decimals, mult equation by 4, results
s^2 + 10s - 120 = 0
:
Use the quadratic formula to solve for s:
In this equation a=1, b=10, c=-120
:
solve this you should get a postive solution of:
s = 7.05 mph is K's walking speed
then
7.05 + 10 = 17.05 mph is B's biking speed
:
:
Confirm this by finding the time of each
3/7.05 = .425 hrs or 25.5 min
3/17.05 = .176 hrs or 10.6 min
---------------
Difference ~ 15 min
|
Evaluation_Word_Problems/161028: two less than one third of a number equals 3 more than fourth of the number. find the number
1 solutions
Answer 118654 by ankor@dixie-net.com(15638) on 2008-10-08 17:53:40 (Show Source):
You can put this solution on YOUR website!two less than one third of a number equals 3 more than fourth of the number. find the number
 x - 2 =  x + 3
Add 2 to both sides:
x = x + 3 + 2
x = x + 5
Multiply equation by 12 to get rid of the denominators:
12* x = 12* x + 12(5)
Results:
4x = 3x + 60
4x - 3x = 60
x = 60
:
:
Check solution original equation:
(60) - 2 = (60) + 3
20 - 2 = 15 + 3
|
Evaluation_Word_Problems/161029: twice the greater of two consecutive odd integers is 13 less than three times the lesser number. find the integers
1 solutions
Answer 118653 by ankor@dixie-net.com(15638) on 2008-10-08 17:48:02 (Show Source):
You can put this solution on YOUR website!Let the two odd consecutive integers be: x, (x+2)
Write an equation for what it says:
"twice the greater of two consecutive odd integers is 13 less than three times the lesser number."
2(x+2) = 3x - 13
2x + 4 = 3x - 13
4 + 13 = 3x - 2x
17 = x
:
The two numbers, 17, 19
:
Check solution in the given statement
2(19) = 3(17) - 13
38 = 51 - 13
|
Length-and-distance/161015: At 9am two bicyclists heading in opposite directions pass eachother on a bicycle path. The bike heading north is riding 8km/hour FASTER than the bike heading south. At 1030 they are 36km apart. Find the two bikes rates and show you got your answers
1 solutions
Answer 118645 by ankor@dixie-net.com(15638) on 2008-10-08 16:13:23 (Show Source):
You can put this solution on YOUR website!At 9am two bicyclists heading in opposite directions pass each other on a bicycle path. The bike heading north is riding 8km/hour FASTER than the bike heading south. At 1030 they are 36km apart. Find the two bikes rates and show you got your answers
:
Let s = speed of the southbound bike
then
(s+8) = speed of the northbound bike
:
Find the travel time (since they met) of the bikes: 10;30 - 9:00 = 1.5 hrs
:
Write a distance equation; Dist = time * speed
:
South dist = north dist = 36 mi
1.5s + 1.5(s+8) = 36
1.5s + 1.5s + 12 = 36
3s = 36 - 12
s = 
s = 8 mph speed of the southbound bike
and
8 + 8 = 16 mph speed of the northbound bike
:
:
Check solution by finding the total distance
1.5(8) + 1.5(16) =
12 + 24 = 36
|
Evaluation_Word_Problems/160902: A photograph that measures 20 cm by 35 cm is to be surrounded by a matte before framing. The
width of the matte will be equal on all four sides. If the area of the matte will be twice the area of
the photograph, determine the width of the matte.
1 solutions
Answer 118641 by ankor@dixie-net.com(15638) on 2008-10-08 15:17:21 (Show Source):
You can put this solution on YOUR website!A photograph that measures 20 cm by 35 cm is to be surrounded by a matte before
framing. The width of the matte will be equal on all four sides.
If the area of the matte will be twice the area of the photograph, determine
the width of the matte.
:
Let x = width of the matte
:
20 * 35 = 700 sq cm is the area of the photo
then
2(700) = 1400 sq cm is the area of the matte
:
The dimension of the matte will be (2x+20) by (2x+35)
:
I am assuming that the matte will not be behind the photo, just around it
Therefore we can find the area using these dimensions, assuming the area will
be 2100 sq cm with 700 sq cm (which is behind the photo) not counted
giving us a matte area of 1400 sq cm
:
(2x + 20) * (2x + 35) = 2100
FOIL
4x^2 + 70x + 40x + 700 = 2100
:
4x^2 + 110x + 700 - 2100 = 0
:
4x^2 + 110x - 1400 = 0
Simplify divide by 2
2x^2 + 55x - 700 = 0
This equation requires the quadratic formula:
In this equation; a=2; b=55; c=-700
:
:
Solve this and you should get a positive solution: x = 9.4677 cm as the width
;
A rough check using a calc: 2x = 19
(20+19*)(35+19) = 2106 cm - 700 (behind the photo) = 1406 sq/cm area of the matte
|
Rate-of-work-word-problems/160986: One person can do a job in 8 hours. A second person can do it in 12 hours. If the first person works 2 hours less than the second, how many hours will it take them working together?
Thanks for your help!
J
1 solutions
Answer 118636 by ankor@dixie-net.com(15638) on 2008-10-08 14:18:58 (Show Source):
You can put this solution on YOUR website!One person can do a job in 8 hours. A second person can do it in 12 hours. If the first person works 2 hours less than the second, how many hours will it take them working together?
:
Let t = time that they worked together
then
(t+2) = total time worked by the 2nd person
:
Let the completed job = 1
;
Each will do a fraction of the work which will add up to 1:
:
1st person + 2nd person = completed job
 +  = 1
:
Multiply equation by 24 to get rid of the denominator, rsults:
3t + 2(t+2) = 24
3t + 2t + 4 = 24
3t + 2t = 24 - 4
5t = 20
t = 
t = 4 hrs working together
;
:
Check solution:
4/8 + 6/12 = 1
|
Age_Word_Problems/160921: Obie told Beth I am twice as old as you were when I was as old as you are. Their ages told 49. How old is each.
1 solutions
Answer 118634 by ankor@dixie-net.com(15638) on 2008-10-08 14:04:07 (Show Source):
You can put this solution on YOUR website!Obie told Beth I am twice as old as you were when I was as old as you are. Their ages told 49. How old is each.
:
Let A = O's age now
Let B = Beth's age now
:
A + B = 49
B = (49-A)
:
Write an equation for this statement:
"Obie told Beth I am twice as old as you were when I was as old as you are."
A = 2(B - (A-B))
A = 2(B - A + B
A = 2(2B-A)
A = 4B - 2A
A + 2A = 4B
3A = 4B
Substitute (49-A) for B
3A = 4(49-A)
3A = 196 - 4A
3A + 4A = 196
A = 
A = 28 yrs old is O's age
Then
49 - 28 = 21 yrs is B's age
:
See if that fits the statement:
Obie told Beth I am twice as old as you were when I was as old as you are.
28 = 2(21 - 7)
28 = 2(14)
|
Word_Problems_With_Coins/160966: Amanda has some pennies, nickels, dimes, and quarters in her piggy bank. There is more than $1.50 and less than $2.25. Using the clues, determine how much money Amanda has.
-there are 4 times as many nickels as quarters
-there are twice as many quarters as dimes
-there is an equal number of pennies and dimes
Thank you for you help!!
1 solutions
Answer 118631 by ankor@dixie-net.com(15638) on 2008-10-08 13:37:28 (Show Source):
You can put this solution on YOUR website!Amanda has some pennies, nickels, dimes, and quarters in her piggy bank. There is more than $1.50 and less than $2.25. Using the clues, determine how much money Amanda has.
:
Write an equation for each statement:
:
"-there are 4 times as many nickels as quarters"
n = 4q
:
"-there are twice as many quarters as dimes"
q = 2d
:
"-there is an equal number of pennies and dimes"
p = d
:
Write a total$ equation within the given range
.01p + .05n + .10d + .25q = 2.00
:
try to get everything in terms of d:
In the 1st equation, substitute 2d or q (from the 2nd equation)
n = 4(2d)
n = 8d
:
Substitute:
.01d + .05(8d) + .10d + .25(2d) = 2.00
.01d + .40d + .10d + .50d = 2
1.01d = 2
d =  obviously not a solution (has to be an integer)
:
Make a solution by multiplying 1.01 * 2, so the total is $2.02, then we have:
d = 
d = 2 dimes
then
.01(2) + .40(2) + .10(2) + .50(2) = 2
.02 + .80 + .20 + 1.00 = $2.02
:
Find the number of each coin using d = 2:
p = d; 2 pennies
n = 8d: 16 nickels
d = 2 dimes
q = 2d; 4 quarters
;
:
Confirm solution from this:
.01(2) + .05(16) + .10(2) + .25(4) =
.02 + .80 + .20 + 1.00 = $2.02 is Amanda's total
:
There are probably other ways to do this. Did this make sense to you?
|
Circles/160972: My worksheet says:
In a circle whose diameter is 20 inches, a chord is 6 inches from the center. What is the length of the chord?
1 solutions
Answer 118628 by ankor@dixie-net.com(15638) on 2008-10-08 13:02:36 (Show Source):
You can put this solution on YOUR website!In a circle whose diameter is 20 inches, a chord is 6 inches from the center. What is the length of the chord?
:
Here is one way. Draw a circle, draw in the chord. See that a triangle is formed
by length of the chord and two radii.
:
This triangle consists of two right triangles where:
hypotenuse = 10" (radius)
one side = 6" distance from chord to the center
one side = 1/2 the length of the chord (x)
:
x^2 + 6^2 = 10^2
x^2 + 36 = 100
x^2 = 100 - 36
x = 
x = 8" is half the chord, therefore the chord = 16"
|
Numbers_Word_Problems/160793: The tens digit of a three-digit number exceeds the hundreds digit by the same amount that the units digit exceeds the tens digit. When the digits are reversed, the new number exceeds the original number by 198. Find the original number.
1 solutions
Answer 118627 by ankor@dixie-net.com(15638) on 2008-10-08 12:48:32 (Show Source):
You can put this solution on YOUR website!The tens digit of a three-digit number exceeds the hundreds digit by the same amount that the units digit exceeds the tens digit. When the digits are reversed, the new number exceeds the original number by 198. Find the original number.
:
Let x=100's digit; y=10's digit; z=units digit
:
"The tens digit of a three-digit number exceeds the hundreds digit by the same amount that the units digit exceeds the tens digit."
The equation for this statement:
y - x = z - y
y + y = x + z
2y = x+z
;
"When the digits are reversed, the new number exceeds the original number by 198."
100z + 10y + x - (100x + 10z + z) = 198
100z + 10y + x - 100x - 10z - z = 198
100z - z + 10y - 10y + x - 100x = 198
99z - 99x = 198
Divide equation by 99:
z - x = 2
z = x + 2
::
In the 1st equation substitute (x+2) for z
2y = x + (x+2)
2y = 2x + 2
Divide equation by 2
y = x + 2
x = y - 2
:
y has to > 2, (x can't = 0) try y = 3, use the two equations to find x and z
original number: 133, reverse number 331
331 - 133 = 198
:
Find the original number.
Here are some more numbers that will work
y=4; 442 - 244 = 198
y=5; 553 - 355 = 198
y=6; 664 - 466 = 198
y=7; 775 - 577 = 198
y=8; 886 - 688 = 198
y=9; 997 = 799 = 198
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Travel_Word_Problems/160740: This question is from textbook
a train leaves the station at 6:00pm traveling west at 80 mi/h. on a parallel track, a second train leaves the station 3 hours later traveling west at 100mi/h. at what time will the second train catch up with the first?
1 solutions
Answer 118590 by ankor@dixie-net.com(15638) on 2008-10-07 21:39:07 (Show Source):
You can put this solution on YOUR website!a train leaves the station at 6:00pm traveling west at 80 mi/h. on a parallel track, a second train leaves the station 3 hours later traveling west at 100mi/h. at what time will the second train catch up with the first?
:
Let t = travel time of the 1st train
then
(t-3) = travel time of the 2nd train
:
When the 2nd train catches the 1st train, they will have traveled the same distance
:
Write a distance equation: Dist = speed * time
:
2nd train dist = 1st train dist
100(t-3) = 80t
:
100t - 300 = 80t
:
100t - 80t = +300
:
20t = 300
t = 
t = 15 hrs, travel time of the 1st train
then
6 PM + 15 hrs = 9 AM on the following day
:
:
Check the solution by confirming that both trains traveled ths same distance
80*15 = 1200 mi
100*12 = 1200 mi
|
Age_Word_Problems/160883: Mary is six years older than her only brother Jaun. Three times Mary's age is 8 more than four times Juan's age. How old is Mary's brother?
3x = 8 + 4x (this is what I got out of this please help me figure this equation out once I figure it out I can solve on my own). Thanks
1 solutions
Answer 118580 by ankor@dixie-net.com(15638) on 2008-10-07 20:46:38 (Show Source):
You can put this solution on YOUR website!Mary is six years older than her only brother Jaun. Three times Mary's age is 8 more than four times Juan's age. How old is Mary's brother?
Do it like this
write an equation for each statement:
"Mary is six years older than her only brother Jaun.
M = J + 6
:
"Three times Mary's age is 8 more than four times Juan's age."
3M = 4J + 8
:
How old is Mary's brother?
From the 1st equation, replace M with (J+6) in the above equation
3(J+6) = 4J + 8
3J + 18 = 4J + 8
18 - 8 = 4J - 3J
J = 10
;
Use the 1st equation to find M, check solution in the 2nd equation
|
Linear_Equations_And_Systems_Word_Problems/160789: please help me solve the problem. Thank you!
the units digits of a two-digit number is 3 more than twice the tens digit. If the digits are reversed, the new number is 9 less than 4 times the original number. Find the original number.
1 solutions
Answer 118575 by ankor@dixie-net.com(15638) on 2008-10-07 20:25:33 (Show Source):
You can put this solution on YOUR website!the units digits of a two-digit number is 3 more than twice the tens digit. If the digits are reversed, the new number is 9 less than 4 times the original number. Find the original number.
;
Let x = the 10's digit
Let y - units digit
then
10x + y = original number
:
Write and equation for each statement:
;
"the units digits of a two-digit number is 3 more than twice the tens digit."
y = 2x + 3
:
"If the digits are reversed, the new number is 9 less than 4 times the original number."
10y + x = 4(10x+y) - 9
10y + x = 40x + 4y - 9
10y - 4y = 40x - x - 9
6y = 39x - 9
:
Find the original number.
:
Substitute (2x+3) for y in the above equation:
6(2x+3) = 39x - 9
12x + 18 = 39x - 9
18 + 9 = 39x - 12x
27 = 27x
x = 1
:
Then using y = 2x+3
y = 2(1) + 3
y = 5
:
Original number = 15
:
:
Check solution in the statement:
"If the digits are reversed, the new number is 9 less than 4 times the original number."
51 = 4(15) - 9
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Percentage-and-ratio-word-problems/160771: A company specializing in magazine sales over the telephone found that in 2500 calls, 360 resulted in sales made by male callers and 480 resulted in sales made by female callers. If the company gets twice as many sales per call with a female voice than with a male voice, how many of the 2500 calls were made by a female?
1 solutions
Answer 118561 by ankor@dixie-net.com(15638) on 2008-10-07 15:53:32 (Show Source):
You can put this solution on YOUR website! A company specializing in magazine sales over the telephone
> found that in 2500 phone calls, 360 resulted in sales and were
> made by male callers, and 480 resulted in sales and were made
> by female callers. If the company gets twice as many sales per
> call with a woman's voice than with a man's voice, then how
> many of the 2500 calls were made by females?
> :
> Let x = no. of girls' call;
> Then (2500-x) = no. of boys' calls
> :
> We can say that percentage of successful calls (sales made) by
> girls is twice the percentage made by boys
> :
>  = % made by girls
:
>  = % made by boys
>
> :
> Girls % = 2 times boys
= 2( )
:
= (  )
> Cross multiply
> 720x = 480(2500-x)
>
> 720x = 1200000 - 480x
>
> 720x + 480x = 1200000
>
> 1200x = 1200000
>
> x = 1200000/1200
>
> x = 1000 calls made by girls
> :
> Check using percentage:
> 480/1000 = 48 %
> 360/1500 = 24 %
>
> Did this make sense to you?
|
Quadratic_Equations/160814: The speed of an airplane in still air is 168 mph. The plane travels 689 miles against the wind and 950 miles with the wind in a total time of 11 hours. What is the speed of the wind.
I have tried everything with this question and I keep getting the wrong answer. I think I am screwing up distributing.
1 solutions
Answer 118558 by ankor@dixie-net.com(15638) on 2008-10-07 15:31:26 (Show Source):
You can put this solution on YOUR website!The speed of an airplane in still air is 168 mph. The plane travels 689 miles
against the wind and 950 miles with the wind in a total time of 11 hours.
What is the speed of the wind.
:
Let x = speed of the wind
then
(168-x) = speed against the wind
and
(168+x) = speed with the wind
:
Write a time equation: Time =
Against wind time + With wind time = 11 hr
 +  = 11
:
Multiply equation by (168+x)(168-x), results:
689(168+x) + 950(168-x) = 11(168+x)(168-x)
:
115752 + 689x + 159600 - 950x = 11(28224 - x^2)
:
-261x + 275352 = 310464 - 11x^2
:
Arrange as quadratic equation on the left
+11x^2 - 261x + 275352 - 310464 = 0
:
11x^2 - 261x - 35112 = 0
:
This nasty equation requires the quadratic formula; a=11; b=-261; c=-35112
You should get positive solution: x ~ 69.6 mph speed of the wind
:
:
We can confirm that:
689/(268-69.6) = 7.00 hrs
950/(268+69.6) = 4.00 hrs
---------------------------
total time = 11 hrs
|
Linear_Algebra/160700: Use elimination method to solve the system.
-4x+4y-2z=-8
-3x-y+4z=0
2x-2y+3z=-4
1 solutions
Answer 118557 by ankor@dixie-net.com(15638) on 2008-10-07 15:02:35 (Show Source):
You can put this solution on YOUR website!-4x + 4y - 2z =-8
-3x - y + 4z = 0
+2x- 2y + 3z =-4
:
The coefficients of the 1st and 3rd equations, will help us alot:
:
Multiply the 3rd equation by 2, and add to the 1st equation
-4x + 4y - 2z = -8
+4x - 4y + 6z = -8
---------------------adding eliminates x and y, find z
0x + 0y + 4z = -16
z = 
z = -4
:
Substitute -4 for z in the 2nd equation
-3x - y + 4(-4) = 0
-3x - y - 16 = 0
-3x - y = 16
:
Substitute -4 for z in the 3rd equation:
+2x - 2y + 3(-4) = -4
+2x - 2y - 12 = -4
+2x - 2y = -4 + 12
+2x - 2y = +8
:
Multiply -3x - y = 16 by -2 and add to the above equaiton
+6x + 2y = -32
+2x - 2y = 8
---------------- addition eliminate y
8x = -24
x = 
x = -3
:
Find y using the 2nd equation, substitute for x & z
-3(-3) - y + 4(-4) = 0
+9 - y - 16 = 0
-y -7 = 0
-y = +7
y = -7
:
Solutions: x=-3, y=-7; z=-4
:
:
Check solutions in the 3rd equation:
+2x- 2y + 3z =-4
2(-3) - 2(-7) + 3(-4) = -4
-6 + 14 - 12 = -4
-18 + 14 = -4
|
Radicals/160696: Solve: 10= ________
V 5m + 1 + 6
(10 equals the square root of 5m+1, plus 6)
Please help with this problem!
1 solutions
Answer 118556 by ankor@dixie-net.com(15638) on 2008-10-07 14:31:18 (Show Source):
You can put this solution on YOUR website!Solve: 10= ________
V 5m + 1 + 6
(10 equals the square root of 5m+1, plus 6)
:
We can write it:
10 = 
:
Subtract 6 from both sides; you have:
4 = 
:
Square both sides, get rid of the radical
16 = 5m + 1
:
Subtract 1 from both sides:
15 = 5m
;
Divide both sides by 5
m = 
m = 3
:
:
Check solution in original equation:
10 = 
:
10 = 
:
10 = 
:
10 = 4 + 6
|
Numbers_Word_Problems/160705: This question is from textbook
In a certain triangle the measure of one angle is double the measure of a second angle but is 5 degrees less than the measure of the third angle. If the sum of the measures of the three interior angles of a triangle is always 180 degrees, form an algebraic equation to express the problem, and identify the variables, coefficients, and constants of the alegbraic expression.
1 solutions
Answer 118554 by ankor@dixie-net.com(15638) on 2008-10-07 14:21:10 (Show Source):
You can put this solution on YOUR website!In a certain triangle the measure of one angle is double the measure of a second angle but is 5 degrees less than the measure of the third angle. If the sum of the measures of the three interior angles of a triangle is always 180 degrees, form an algebraic equation to express the problem, and identify the variables, coefficients, and constants of the algebraic expression.
:
Let the angles be A, B, C
:
Write an equation for each statement:
:
"the measure of one angle is double the measure of a second angle"
A = 2B
or
B = .5A
:
" but is 5 degrees less than the measure of the third angle."
A = C-5
or
C = (A+5)
:
"If the sum of the measures of the three interior angles of a triangle is always 180 degrees,":
A + B + C = 180
:
form an algebraic equation to express the problem, and identify the variables, coefficients, and constants of the algebraic expression.
:
Substitute for B and C
A + .5A + (A+5) = 180
2.5A = 180 - 5
2.5A = 175
solve
A = 
A = 70 degrees, B = 35, C = 75
|
Linear-systems/160725: This question is from textbook Algebra 1
A migrating elephant herd started moving at a rate of 6 miles per hour. One stood still and was left behind. He got nervous and began running at 10 miles per hour. He caught up to the herd in 5 minutes. How far did he run? How long in hours did he run?
1 solutions
Answer 118549 by ankor@dixie-net.com(15638) on 2008-10-07 14:01:18 (Show Source):
You can put this solution on YOUR website!A migrating elephant herd started moving at a rate of 6 miles per hour. One stood still and was left behind. He got nervous and began running at 10 miles per hour. He caught up to the herd in 5 minutes. How far did he run? How long in hours did he run?
:
Change 5 min to hrs;  = .083 hrs
:
Dist = time * speed
.083 * 10 = .83 miles ran the lone elephant to catch up
|
Money_Word_Problems/160728: The members of a flying club plan to share equally the cost of a $200,000 airplane. The members want to 5 more people to join the club so that the cost per person will decrease by $2,000. How many members are currently in the club?
1 solutions
Answer 118529 by ankor@dixie-net.com(15638) on 2008-10-07 09:58:15 (Show Source):
You can put this solution on YOUR website! (2008-10-06 21:30:37): The members of a flying club plan to share equally the cost of a $200,000 airplane. The members want to 5 more people to join the club so that the cost per person will decrease by $2,000. How many members are currently in the club?
:
We can deal with this in $1000's Plane cost $200, cost decrease is $2
:
Let x = no. members currently in the club
then
 = cost per member now
and
 = cost if 5 more members join
:
The equation:
- 2 =
:
Multiply equation by x(x+5), results
200(x+5) - 2(x(x+5) = 200x
200x + 1000 - (2x^2 + 10x) = 200x
:
200x + 1000 - 2x^2 - 10x - 200x = 0
:
-2x^2 - 10x + 1000 = 0
:
Simplify divide equation by -2
+x^2 + 5x - 500 = 0
Factor
)x-20)(x+25) = 0
Positive solution
x = 20 members currently
:
:
Check solution find the actual costs
200000/20 = $10000
200000/25 = $8000
|
Travel_Word_Problems/160643: A plane flew a distance of 1555 miles in 5 hours. During the first 3 hours of the flight, it flew with a wind a distance of 975 miles. During the remainder of the flight, the plane flew against a wind whose average was 5 mph less than what it had been during the first part of the flight. Find the rate of the plane in still air and the original speed of the wind.
Some helpful equations:
r= the rate in still air
c= the rate of the air current
r+c= rate traveling with the current
r-c= rate traveling against the current
1 solutions
Answer 118495 by ankor@dixie-net.com(15638) on 2008-10-06 21:44:10 (Show Source):
You can put this solution on YOUR website!A plane flew a distance of 1555 miles in 5 hours. During the first 3 hours of
the flight, it flew with a wind a distance of 975 miles. During the remainder
of the flight, the plane flew against a wind whose average was 5 mph less than
what it had been during the first part of the flight. Find the rate of the
plane in still air and the original speed of the wind.
:
Some helpful equations:
r= the rate in still air
c= the rate of the air current
r+c= rate traveling with the current
r-c= rate traveling against the current
:
Summarizing what we know:
:
1st part of the trip 975 mi in 3 hrs, at a speed (r+c)
2nd part of the trip: 1555-975 = 580 mi in 5-3 = 2 hrs at a speed (r - (c-5))
:
Write a distance equation for each part of the trip: (Dist = time * speed)
:
3(r+c) = 975
2(r- (c-5)) = 580; wind given as 5 mph less
:
Simplify: divide the 1st equation by 3, and the 2nd equation by 2 and you have;
r + c = 325
and
r - c + 5 = 290
r - c = 290 - 5
r - c = 285
:
Use these two equation for elimination
r + c = 325
r - c = 285
----------------addition eliminate c, find r
2r = 610
r = 305 mph in still air
:
Find the original speed of the wind using r + c = 325
305 + c = 325
c = 20 mph is the wind on the 1st part of the trip
:
:
Check solution by finding the distances
3(305+20) = 975
2(305-15) = 580 (wind is 5 mph less)
----------------
total dist 1555mi
|
Numbers_Word_Problems/160673: The product of two numbers is 330. The smaller number is seven less than the larger number. What are the numbers?
1 solutions
Answer 118483 by ankor@dixie-net.com(15638) on 2008-10-06 19:32:00 (Show Source):
You can put this solution on YOUR website!The product of two numbers is 330. The smaller number is seven less than the
larger number. What are the numbers?
:
Two numbers x, y
:
"The product of two numbers is 330."
x*y = 330
:
"The smaller number is seven less than the larger number."
y = x-7
;
What are the numbers?
:
Substitute (x-7) for y in the 1st equation, solve for x
x(x-7) = 330
x^2 - 7x = 330
x^2 - 7x - 330 = 0
Factor
(x-22)(x+15) = 0
Two solutions
x = +22 then y = +15
x = -15 then y = -22
:
You can check them in the original equations
|
Travel_Word_Problems/160682: In a horse race, Snail is 44 feet behind Cat. While Cat is racing at a steady spped of 48 feet per second. Snail has sped up to 56 feet per second. At these speeds how long will it take for snail to catch up to Cat?
I Know "t*r=d" but how does it apply to this?
1 solutions
Answer 118480 by ankor@dixie-net.com(15638) on 2008-10-06 19:19:57 (Show Source):
You can put this solution on YOUR website!In a horse race, Snail is 44 feet behind Cat. While Cat is racing at a steady
speed of 48 feet per second. Snail has sped up to 56 feet per second.
At these speeds how long will it take for snail to catch up to Cat?
:
Time = 
:
Use the relative speed to find out how long it will take to cover 44 ft
:
Time =  =  = 5.5 seconds
|
Geometry_Word_Problems/160541: find the value of k so that the line through (4,k) and (-2,-1) is parallel to y=-2x+3/2
1 solutions
Answer 118474 by ankor@dixie-net.com(15638) on 2008-10-06 17:54:39 (Show Source):
You can put this solution on YOUR website!find the value of k so that the line through (4,k) and (-2,-1) is parallel to y=-2x+3/2
:
Parallel lines have the same slope, therefore the slope of the line: m= -2
:
Use the slope formula m = 
:
Assign the given coordinate as follows:
x1 = 4; y1 = k
x2 =-2; y2 = -1
m =-2
:
 = -2
:
 = -2
:
Multiply both sides by -6, results
-1 - k = -6(-2)
:
-1 - k = +12
:
-k = 12 + 1
:
-k = +13
or
k = -13
;
Find the equation for this line, so we can check he given coordinates:
y - (-13) = -2(x - 4)
y + 13 = -2x + 8
y = -2x + 8 - 13
y = -2x - 5
If substitute the given values for x, we get the given value for y
|
Travel_Word_Problems/160640: Jones can run around a 400-meter track in 65 seconds. How long does Smith take to run the 400 meters if he meets Jones in 35 seconds after they start together in a race around the track in opposite directions?
Not sure how to set up the equation for this problem.
1 solutions
Answer 118460 by ankor@dixie-net.com(15638) on 2008-10-06 16:28:59 (Show Source):
You can put this solution on YOUR website!Jones can run around a 400-meter track in 65 seconds. How long does Smith take
to run the 400 meters if he meets Jones in 35 seconds after they start together
in a race around the track in opposite directions?
:
When they meet, they will have traveled a total of 400 meters in 35 seconds
:
Find Jone's speed in meters/sec:  = 6.154 m/sec
:
Let s = Smith's speed in m/sec
:
Write a dist equation; Dist = time * speed
:
35s + 35(6.154) = 400
:
35s + 215.39 = 400
:
35s = 400 - 215.39
:
35s = 184.61
s = 
s = 5.275 m/sec is Smith's speed
:
Find time for Smith to run 400 m:
 = 75.83 sec to run 400 m
:
:
Check solution:
35 * 5.275 = 184.625 m
35 * 6.154 = 215.39
------------------
Total dist = 400.0
|
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