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15390..15419 , 15420..15449 , 15450..15479 , 15480..15509 , 15510..15539 , 15540..15569 , 15570..15599 , 15600..15629 , 15630..15659, >>NextMixture_Word_Problems/695784: Mrs. Thomas walked 160 feet on a moving walkway in 40 seconds. Against the walkway she was able to walk the same distance in 80 seconds. What is the rate of the escalator? (How fast)
What is Mrs. Thomas' normal rate? (How fast)
1 solutions
Answer 429051 by ankor@dixie-net.com(15660)   on 2012-12-21 20:45:03 (Show Source):
You can put this solution on YOUR website!Mrs. Thomas walked 160 feet on a moving walkway in 40 seconds.
Against the walkway she was able to walk the same distance in 80 seconds.
What is the rate of the escalator? (How fast)
What is Mrs. Thomas' normal rate? (How fast)\
:
let w = the normal walking rate
let e = the escalator rate
then
(w+e) = the effective rate walking with the escalator
and
(w-e) = the effective rate walking against the escalator
:
Write a distance equation for each scenario
:
40(w+e) = 160
and
80(w-e) = 160
:
Simplify both equation; divide the 1st one by 40, the 2nd one by 80, results:
w + e = 4
w - e = 2
-----------adding eliminates e find w
2w = 6
w = 3 ft/sec is the normal walk rate
then
3 + e = 4
e = 4 -3
e = 1 ft/sec is the escalator rate
:
:
You can confirms this in both original equations
|
Rate-of-work-word-problems/696478: Suppose I paint a wall in 10 hours, and you and I together paint a wall in 2 hours. How much faster do you paint a wall than I?
1 solutions
Answer 429046 by ankor@dixie-net.com(15660) on 2012-12-21 19:21:45 (Show Source):
You can put this solution on YOUR website! Suppose I paint a wall in 10 hours, and you and I together paint a wall in 2 hours.
How much faster do you paint a wall than I?
:
Let t = time for you to paint the wall
:
Let the completed job = 1 (A painted wall)
:
A shared work equation
 +  = 1
Multiply by 10t, results
2t + 10(2) = 10t
20 = 10t - 2t
20 = 8t
t = 20/8
t = 2.5 hrs
:
10 - 2.5 = 7.5 hrs faster
|
Linear_Equations_And_Systems_Word_Problems/696362: Please answer my question: If 6 kilos of oranges and 5 kilos of apples cost 419 while 5 kilos of oranges and 7 kilos of apples cost 488, what is the cost of each per kilo?
1 solutions
Answer 429043 by ankor@dixie-net.com(15660) on 2012-12-21 19:05:30 (Show Source):
You can put this solution on YOUR website!If 6 kilos of oranges and 5 kilos of apples cost 419 while 5 kilos of oranges
and 7 kilos of apples cost 488, what is the cost of each per kilo?
:
Let x = cost of oranges per kilo
Let y = cost of apples
:
write an equation for each transaction
6x + 5y = 419
5x + 7y = 488
:
Use elimination here, mult the 1st eq by 7 and the 2nd eq by 5
42x + 35y = 2933
25x + 35y = 2440
-------------------subtraction eliminates y, find x
17x = 493
x = 493/17
x = 29 is the cost of the oranges
;
You can find the cost of the apples, substitute 29 for x in one of the equations and find y.
Check your solutions in the other equation.
|
Polynomials-and-rational-expressions/696359: Steve is two thirds as old as Alex. In seven years, Steve will be three fourths as old as Alex. How old are they now?
1 solutions
Answer 429021 by ankor@dixie-net.com(15660) on 2012-12-21 16:48:09 (Show Source):
You can put this solution on YOUR website!Steve is two thirds as old as Alex.
In seven years, Steve will be three fourths as old as Alex.
How old are they now?
:
let s = Steve's present age
Let a = Alex's age
:
Write an equation for each statement
:
"Steve is two thirds as old as Alex."
s =  a
get rid of the fraction, mult both side by 3
3s = 2a
3s - 2a = 0
:
" In seven years, Steve will be three fourths as old as Alex."
s + 7 =  (a+7)
mult both sides by 4
4(s+7) = 3(a + 7)
4s + 28 = 3a + 21
4s - 3a = 21 - 28
4s - 3a = -7
:
Use elimination here, mult the 1st equation by 3, the 2nd equation by 2
9s - 6s = 0
8s - 6a = -14
---------------subtraction eliminates a, find s
s = 14 yrs is Steve's age
then
3(14) - 2(a) = 0
42 - 2a = 0
-2a = -42
a = 21 yrs is Alex's age
;
:
Confirm this in the statement:
"In seven years, Steve will be three fourths as old as Alex."
14 + 7 = (21+7)
21 = (28)
|
Equations/696394: Paul and James go out for a cycle and are 16 km from home when Paul runs into a tree damaging his bicycle beyond repair. They decide to return home and that Paul will start on foot and James will start on his bicycle. After some time, James will leave his bicycle beside the road and continue on foot, so that when Paul reaches the bicycle he can mount it and cycle the rest of the distance. Paul walks at 4 km/h and cycles at 10 km/h, while James walks at 5 km/h and cycles at 12 km/h. For what length of time should James ride the bicycle, if they are both to arrive home at the same time?
1 solutions
Answer 429019 by ankor@dixie-net.com(15660) on 2012-12-21 15:46:39 (Show Source):
You can put this solution on YOUR website! Paul and James go out for a cycle and are 16 km from home when Paul runs into a tree damaging his bicycle beyond repair.
They decide to return home and that Paul will start on foot and James will start on his bicycle.
After some time, James will leave his bicycle beside the road and continue on foot, so that when Paul reaches the bicycle he can mount it and cycle the rest of the distance.
Paul walks at 4 km/h and cycles at 10 km/h,
while James walks at 5 km/h and cycles at 12 km/h.
For what length of time should James ride the bicycle, if they are both to arrive home at the same time?
:
We know that while one is riding the other is walking and vice-versa
:
Let x = James riding time, this is also Paul's walking time
Let y = Paul's riding time, this also James walking time
:
Write a distance equation for each guy
James: 12x + 5y = 16
Paul: 4x + 10y = 16
:
multiply the 1st equation by 2, subtract the 2nd
24x + 10y = 32
4x + 10y = 16
-----------------
20x = 16
x = 16/20
x = .8 hrs James's time riding
:
Both will take .8 + 1.28 = 2.08 hrs to complete the trip of 16 km
:
To check this, find y using the 2nd equation 4x + 10y = 16
4(.8) + 10y = 16
3.2 + 10y = 16
10y = 16 - 3.2
10y = 12.8
y = 12.8/10
y = 1.28 hrs
:
Check this in the James equation
12(.8) + 5(1.28) =
9.6 + 6.4 = 16 mi
and in the Paul's equation
4(.8) + 10(1.28) =
3.2 + 12.8 = 16 mi; confirms our solution of James riding for .8 hrs
|
Equations/696382: X can do 1/8th of work in 10 day Y can do 60% of the work in 60 days and Z can do 1/5 of work in 15 day who will complete the work first
1 solutions
Answer 429015 by ankor@dixie-net.com(15660) on 2012-12-21 15:18:29 (Show Source):
You can put this solution on YOUR website! X can do 1/8th of work in 10 day Y can do 60% of the work in 60 days and Z can do 1/5 of work in 15 day who will complete the work first
:
Find how long for each to complete the job
:
x: 8 * 10 = 80 days
:
y: .6d = 60
d = 60/.6
d = 100 days
:
Z: 5 * 15 = 75 days
|
Percentage-and-ratio-word-problems/696364: A father and his son can do a job in 20 days. The father can do four times as much work as his son in a given amount of time. In how many days can the father do the job alone?
1 solutions
Answer 428983 by ankor@dixie-net.com(15660) on 2012-12-21 10:28:54 (Show Source):
You can put this solution on YOUR website!A father and his son can do a job in 20 days.
The father can do four times as much work as his son in a given amount of time.
In how many days can the father do the job alone?
:
let d = time required by Dad working alone
then
4d = time required by sonny
:
let the completed job = 1
:
Each will do a fraction of the job, the two fractions add up to one.
:
 +  = 1
multiply by 4d
4(20) + 20 = 4d
100 = 4d
d = 100/4
d = 25 days dad alone
:
:
Check this, son's time 4(25)
 + 
.8 + .2 = 1
|
Equations/696393: A man can walk at 4 km/h or jog at 6 km/h . He is going to a place 30 km away. He can cover half of the distance by walking and the other half by jogging. He can also walk half of the time and jog half of the time. Which method takes less time, and by how much lesser?
1 solutions
Answer 428982 by ankor@dixie-net.com(15660) on 2012-12-21 10:21:59 (Show Source):
You can put this solution on YOUR website! A man can walk at 4 km/h or jog at 6 km/h . He is going to a place 30 km away. He can cover half of the distance by walking and the other half by jogging. He can also walk half of the time and jog half of the time. Which method takes less time, and by how much lesser?
:
Find the time walking half and jogging half; time = dist/speed
t =  + 
t =  + 
t = 55/12
t = 4.458 hrs
:
Find the time,jogging half the time, walking half the time
let t = total time, write a distance equation; dist = speed * time
.5t(4) + .5t(6) = 30
2t + 3t = 30
5t = 30
t = 30/5
t = 6 hrs
|
Age_Word_Problems/695938: I have 3 cousins on my dad's side. The product of their ages is 84. Next year the youngest will be 1/4 the age of the middle cousin. In 2 years from now, the oldest will be twice the current age of the middle. What is the age of my oldest cousin?
Can you please explain how you got the answer please. I'm in 4th grade and I want to learn how to solve it.
Thank you.
1 solutions
Answer 428981 by ankor@dixie-net.com(15660) on 2012-12-21 10:07:40 (Show Source):
You can put this solution on YOUR website!I have 3 cousins on my dad's side. The product of their ages is 84.
Next year the youngest will be 1/4 the age of the middle cousin.
In 2 years from now, the oldest will be twice the current age of the middle.
What is the age of my oldest cousin?
:
Let the cousins' ages be a, b, c; a is the oldest
:
Write an equation for each statement
:
"The product of their ages is 84."
a * b * c = 84
:
" Next year the youngest will be 1/4 the age of the middle cousin."
c + 1 =  (b+1)
From this we know b + 1 is a multiple of 4, (we only have integers here)
And it has to be a factor of 84
b = 3, does not work try: b = 7
c + 1 = (7+1)
c + 1 = 8
c + 1 = 2
c = 2 - 1
c = 1
:
" In 2 years from now, the oldest will be twice the current age of the middle."
a + 2 = 2b
a + 2 = 2(7)
a = 14 - 2
a = 12
:
We have a = 12, b = 7, c = 1
12 * 7 * 1 = 84
:
What is the age of my oldest cousin? 12 yrs old
:
:
That's pretty hard for 4th grade!!
|
Permutations/695935: If only digits 0,1,2,3,4,5,6 maybe used, find the number of possibilities in each category:
a) three-digit numbers
b) odd three-digit numbers
c) three-digit numbers without repeated digitits
1 solutions
Answer 428951 by ankor@dixie-net.com(15660) on 2012-12-20 21:46:01 (Show Source):
You can put this solution on YOUR website! If only digits 0,1,2,3,4,5,6 maybe used, find the number of possibilities in each category:
:
Assuming the 1st digit cannot be 0, first digit has 6 choices
a) three-digit numbers, digits can be repeated
6*7*7 = 294
:
b) odd three-digit numbers
6*7*3 = 126
:
c) three-digit numbers without repeated digitits
6*6*5 = 180
:
Just what is "digitits" something to do with breast implants, perhaps?
|
Graphs/696113: Tara and jada are hiking up a hill. Each has a different stride. The run for Tara's stride is 32 inches, and the rise is 8 inches. The run for jade's stride is 36 inches. What is the rise of jade's stride?
1 solutions
Answer 428949 by ankor@dixie-net.com(15660) on 2012-12-20 21:32:59 (Show Source):
You can put this solution on YOUR website!Tara and jada are hiking up a hill. Each has a different stride.
The run for Tara's stride is 32 inches, and the rise is 8 inches.
The run for jade's stride is 36 inches.
What is the rise of jade's stride?
:
Assuming the relationship of rise and run is same for each hiker
:
 = 
Cross multiply
32r = 8*36
32r = 288
r = 288/32
r = 9 inches is J's rise
|
Average/695863: 10 cows or 25 goats can graze a field in 20 days.How long would 12 cows and 15 goats take to graze the same field?
1 solutions
Answer 428893 by ankor@dixie-net.com(15660) on 2012-12-20 17:13:23 (Show Source):
You can put this solution on YOUR website!10 cows or 25 goats can graze a field in 20 days.
From this we can say a field can be grazed in:
200 cow-days
or
500 goat days
:
How long would 12 cows and 15 goats take to graze the same field?
let d = no. of days with the above animals
let the the grazed field = 1
:
 +  = 1
Multiply by 1000 to clear the denominators, results:
5(12d) + 2(15d) = 1000
60d + 30d = 1000
90d = 1000
d = 1000/90
d = 11.1 days
|
Average/696181: I have a 86 average and took a semester test that is worth 20% of my grade what do I have to make on it to have a 90 or above average?
1 solutions
Answer 428841 by ankor@dixie-net.com(15660) on 2012-12-20 10:56:49 (Show Source):
You can put this solution on YOUR website! I have a 86 average and took a semester test that is worth 20% of my grade
what do I have to make on it to have a 90 or above average?
:
That means 4/5 of your grade is 86, find the 1/5
let x = test grade
 => 90
Mult by 5
344 + x => 450
x => 450 - 344
x => 106, so guess it is not possible
|
Mixture_Word_Problems/696081: The price P (in dollars) that a radio manufacturer is able to charge for a radio is given by P =40-4x^2 where x is the number (in millions) produced. It costs the company $15 to make a radio.
a.) Write an expression for the company's total revenue in terms of x (Could you explain the process for finding this expression?)
b.) Write a function for the company's profit P by subtracting the total cost to make x radios from the expressions in Part A(the one just found)
c.) Currently, the company produces 1.5 million raidos and makes a profit of $24,000,000. Write and solve an equation to find a lesser number of radios that the company could sell and still make a profit.
d.) Do all the solutions in part c make sense in this situation? Explain.
----
Sorry for the long word problem, but I would appreciate it if someone responds
Thank You
1 solutions
Answer 428798 by ankor@dixie-net.com(15660) on 2012-12-19 21:55:25 (Show Source):
You can put this solution on YOUR website!The price P (in dollars) that a radio manufacturer is able to charge for a radio is given by P =40-4x^2 where x is the number (in millions) produced.
It costs the company $15 to make a radio.
:
a.) Write an expression for the company's total revenue in terms of x (Could you explain the process for finding this expression?)
:
Revenue = no. of radios sold * price of the radio
R(x) = x(40-4x^2)
R(x) = -4x^3 + 40x
:
:
b.) Write a function for the company's profit P by subtracting the total cost to make x radios from the expressions in Part A(the one just found)
:
Profit = Revenue - the total cost, (15x is the cost of all the radios sold)
P(x) = -4x^3 + 40x - 15x
P(x) = -4x^3 + 25x
:
:
c.) Currently, the company produces 1.5 million radios and makes a profit of $24,000,000.
Write and solve an equation to find a lesser number of radios that the company could sell and still make a profit.
:
Assume they make 1 million radios,
equation is in millions of radios and millions of dollars
P(x) = -4x^3 + 25x
x = 1 (million)
P(x) = -4(1^3) + 25(1)
P(1) = -4 + 25
P(x) = $21 million in profit when they make 1 million radios
;
d.) Do all the solutions in part c make sense in this situation? Explain.
:
Graphically we can explain it easily,
y = millions of dollars profit, x = millions of radios sold
Green line is $21 million
Looks like max profit occurs when 1.5 million are sold, do you agree?
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Travel_Word_Problems/695774:
On Monday, Roger drove to work in 38 minutes. On Tuesday, he averaged 10 miles per hour more, and it took him 5 minutes less to get to work. How far (in miles) does he travel to work?
1 solutions
Answer 428774 by ankor@dixie-net.com(15660) on 2012-12-19 20:30:22 (Show Source):
You can put this solution on YOUR website!On Monday, Roger drove to work in 38 minutes.
On Tuesday, he averaged 10 miles per hour more, and it took him 5 minutes less to get to work.
How far (in miles) does he travel to work?
:
Find his speed first
:
The dist is the same each day, write a distance equation dist = time * speed
we have to change the minutes to hours
:
 s =  *(s+10)
multiply both sides by 60
38s = 33(s + 10)
38s - 33s = 330
5s = 330
s = 330/5
s = 66 mph on Monday
and
76 mph on Tuesday
:
Find the distance
(66) = 41.8 miles
check that the distance is the same on Tuesday
(76) = 41.8 miles
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Linear-systems/695813: The sums of the digits of a two digit number is 14. If 4 is added to the number, the result is seven times the units digit. find the number?
I have tried solving this problem like 15 times and i still have't come up with the correct answer please help me understand how to do this problem and how to write the equation
1 solutions
Answer 428729 by ankor@dixie-net.com(15660) on 2012-12-19 15:54:09 (Show Source):
You can put this solution on YOUR website!let t = the ten's digit
let u = the units
then
10t + u = "the number"
:
Write an equation for each statement:
:
"The sums of the digits of a two digit number is 14."
t + u = 14
u = (14-t); we can use this form for substitution
:
"If 4 is added to the number, the result is seven times the units digit."
(10t+u) + 4 = 7u
10t + 4 = 7u - u
10t + 4 = 6u
replace u with (14-u) from the 1st statement equation
10t + 4 = 6(14-t)
10t + 4 = 84 - 6t
10t + 6t = 84 - 4
16t = 80
t = 80/16
t = 5 is the 10's digit
then
14 - 5 = 9 is the units
:
59 is the number
:
:
Confirm this in the 2nd statement;
"If 4 is added to the number, the result is seven times the units digit."
4 + 59 = 7(9)
:
Was this understandable for you?
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Polynomials-and-rational-expressions/695453: so I am unsure how to do this. the worksheet says "find the real number solutions" and then gives me these equations
8x^4-x=0
and
x^4=7x^2-18=0
if you could explain how to do that it would be much appreciated
1 solutions
Answer 428547 by ankor@dixie-net.com(15660) on 2012-12-18 11:50:37 (Show Source):
You can put this solution on YOUR website!find the real number solutions
:
8x^4 - x = 0
Factor out x
x(8x^3 - 1) = 0
this is difference of cubes, and can be factored
x(2x-1)(4x^2 + x + 1)
Two real solutions; (4x^2+x+1) will not yield a real solution)
x = 0
and
2x = 1
x = .5
:
and
x^4 + 7x^2 - 18 = 0
Factors to
(x^2 + 9)(x^2 - 2) = 0
Two real solutions, (x^2+9) will not yield real solutions
x^2 = 2
x = + 
and
x = -
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Age_Word_Problems/695508: This problem has been bugging me for ages. I'm having trouble proving this WITHOUT proving by example. Cover all cases.
A worker is paid every other week on Friday. Prove that in some month the worker is paid three times.
1 solutions
Answer 428543 by ankor@dixie-net.com(15660) on 2012-12-18 09:44:41 (Show Source):
You can put this solution on YOUR website!we know that there are 365/7 = 52 weeks in a year, which is 52/2 = 26 pay days in 1 year. There are 12 months, so 10 months must have 2 pay days and 2 months have 3 pay days, for a total of 26
Isn't that proof?
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Travel_Word_Problems/695260: A battleship started at 7:00 AM on a 500 mile voyage on a special mission but was brought to a full stop an hour after starting for military reasons, delaying it for a full hour, after which it was ordered to proceed at a reduced velocity equivalent to 75% of its original speed. This ship arrived at its destination 3 ¾ hr. after the scheduled time. Determine the original speed of the battleship.
1 solutions
Answer 428490 by ankor@dixie-net.com(15660) on 2012-12-17 22:00:18 (Show Source):
You can put this solution on YOUR website!A battleship started at 7:00 AM on a 500 mile voyage on a special mission
but was brought to a full stop an hour after starting for military reasons,
delaying it for a full hour, after which it was ordered to proceed at a reduced
velocity equivalent to 75% of its original speed.
This ship arrived at its destination 3 ¾ hr. after the scheduled time.
Determine the original speed of the battleship.
:
Let s = original speed of the ship
:
change 3 to 3.75 hrs
:
 = time of voyage with no stops or change in speed
:
Write a distance equation of the actual voyage
:
dist at normal speed + distance at reduced speed = 500 mi
1s + .75s( - 1 + 3.75) = 500
1s + .75s( + 2.75) = 500
1s + (.75s( ) + .75s(2.75) = 500
1s + 375 + 2.0625s = 500
3.0625s = 500 - 375
3.0625s = 125
s = 125/3.0625
s = 40.8 mph (or knots if nautical miles are used)
:
:
See if that checks out
normal time: 500/40.8 = 12.25 hrs
Additional time required 3.75 hrs
------------------------------------
Actual time of the voyage: 16 hrs
:
(500-40.8) = 459.2 mi at 3/4 speed which is .75(40.8) = 30.6 knots
 = 15 hr + 1 hr at normal speed = 16 hrs, the actual time
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test/695101: The average age of a husband, wife and their son, 3 years ago was 27 years and that of the wife and son 5 years ago was 21 years. The husband’s present age is ??
1 solutions
Answer 428388 by ankor@dixie-net.com(15660) on 2012-12-17 16:31:18 (Show Source):
You can put this solution on YOUR website!let h = husband's present age
let w = wife's
let s = son's
:
Write an equation for each statement:
:
The average age of a husband, wife and their son, 3 years ago was 27 years
 = 27
Multiply both sides by 3
h + w + s - 9 = 3(27)
h + w + s = 81 + 9
h + w + s = 90
:
and that of the wife and son 5 years ago was 21 years.
 = 21
mult by 2
w + s - 10 = 2(21)
w + s = 42 + 10
w + s = 52
:
In the 1st equation, replace w + s with 52
h + 52 = 90
h = 90 - 52
h = 38 yrs is the husband's age
:
:
Check this
 = 27
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Age_Word_Problems/694902: Please help me solve word problem:
Given that a father's age is 1 less than twice that of his son, and that the digits AB making up the father's age are reversed in the son's age (i.e. BA).
How old are the father and son?
1 solutions
Answer 428278 by ankor@dixie-net.com(15660) on 2012-12-16 21:15:48 (Show Source):
You can put this solution on YOUR website!Given that a father's age is 1 less than twice that of his son,
and that the digits AB making up the father's age are reversed in the son's age
(i.e. BA).
How old are the father and son?
:
Let a = the 10's digit of father's age
Let b = the ones
then
(10a+b) = his age
and
(10b+a) = son's age (digits reversed
:
"Given that a father's age is 1 less than twice that of his son,"
10a + b = 2(10b+a) - 1
10a + b = 20b + 2a - 1
combine like terms
10a - 2a = 20b - b - 1
8a = 19b - 1
divide by 8
a =  b - 
Find a single digit value for b that will give an integer value for a
After a couple of attempts came up with:
b = 3
a = (3) -
a =  -
a = 
a = 7
then
Dad's age = 73
Son's age = 37
:
Check that: 2(37) - 1 = 73
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Miscellaneous_Word_Problems/694931: Suppose you enter an elevator at a certain floor. The elevator moves up 6 floors, down 4 floors, and up 2 floors. You are then at floor 7. At which floor did you initially enter the elevator?
1 solutions
Answer 428253 by ankor@dixie-net.com(15660) on 2012-12-16 19:24:32 (Show Source):
You can put this solution on YOUR website! Suppose you enter an elevator at a certain floor.
The elevator moves up 6 floors, down 4 floors, and up 2 floors.
You are then at floor 7. At which floor did you initially enter the elevator?
:
Let x = floor that you initially entered
:
x + 6 - 4 + 2 = 7
x + 4 = 7
x = 7 - 4
x = 3rd floor
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Age_Word_Problems/694951: seven years ago jackson's age was 2/5 of the age he will be 20 years from now. how old is jackson now
1 solutions
Answer 428252 by ankor@dixie-net.com(15660) on 2012-12-16 19:18:08 (Show Source):
You can put this solution on YOUR website! seven years ago Jackson's age was 2/5 of the age he will be 20 years from now.
j - 7 =  (j+20)
j - 7 = .4(j+20)
j - 7 = .4j + 8
j - .4j = 8 + 7
.6j = 15
j = 15/.6
j = 25 yrs old now
:
You can confirm this solution in the original statement
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Money_Word_Problems/694897: A bank in houston loans $40,000 to a business at 12.5 % annual simple interest for 15 months. How much interest will the bank earn?
The answer I got was $6500. I gues the answer really was $6250. I multiplied the 40,000 by 12.5% and then multiplied that by 1.3 for the 15 months. That is where I messed up. I know 12 months is a year, but I am having troubles with it. Can you please help me understand?
1 solutions
Answer 428244 by ankor@dixie-net.com(15660) on 2012-12-16 16:59:21 (Show Source):
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�t�e�s�t/694549: The city of Ottawa has provided 300 meters of rope to enclose a rectangular swimming area along the shore of the Mooney Bay Beach. What is the maximum area that can be enclosed and the dimensions of the maximum area.
Can you please help me out I really don't understand? Thanks in advance I appreciate it.
1 solutions
Answer 428243 by ankor@dixie-net.com(15660) on 2012-12-16 16:54:35 (Show Source):
You can put this solution on YOUR website!The city of Ottawa has provided 300 meters of rope to enclose a rectangular swimming area along the shore of the Mooney Bay Beach. What is the maximum area that can be enclosed and the dimensions of the maximum area.
:
Let L = the length of the rectangle
Let W = the width
:
Only 3 sides are required so the perimeter with 300 m of rope will be:
L + 2W = 300
L = (300-2W); use this form for substitution in the area equation
:
A = L * W
Replace L with (300-2W)
A = W(300-2W)
A = -2W^2 + 300W
this is a quadratic equation, max area occurs at the axis of symmetry which we can find with formula x = -b/(2a), in this equation it's
W = 
W = 
W = +75 m is the width for max area
then
L = 300 - 2(75)
L = 300 - 150
L = 150 m is the length
Find the area
150 * 75 = 11,250 sq/m is the max area with 300 ft of rope
:
How about this? Are you understanding this now?
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absolute-value/694536: How do u solve a problem like a Effiel tower is 324 meters tall and has a base of 125 meters by 125 . The model will rest on a base with dimensions 5cm by 5cm. How tall will the model be in centimeters?
1 solutions
Answer 428238 by ankor@dixie-net.com(15660) on 2012-12-16 16:31:56 (Show Source):
You can put this solution on YOUR website!Effiel tower is 324 meters tall and has a base of 125 meters by 125 .
The model will rest on a base with dimensions 5cm by 5cm.
How tall will the model be in centimeters?
:
Write a ratio equation
 = 
cross multiply
125h = 5 * 324
125h = 1620
h = 
h ~ 13 cm high
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Word_Problems_With_Coins/694642: Stella is looking for the coins that fell through the hole in her pocket. Together the 12 coins are worth $1.75. She remembers that there are four different kinds of coins. She had 3 times as many of one kind as another kind. what coins could Stella have lost?
1 solutions
Answer 428111 by ankor@dixie-net.com(15660) on 2012-12-15 21:33:40 (Show Source):
You can put this solution on YOUR website!Stella is looking for the coins that fell through the hole in her pocket.
Together the 12 coins are worth $1.75.
4 unknowns here, have to make some logical assumptions
:
p + n + d + q = 12
and
.01p + .05n + .10d + .25q = 1.75
:
She had 3 times as many of one kind as another kind.
Assume
q = 3n
:
Assume 5 pennies, (has to be a multiple of 5, & 10 would only leave 2 more coins)
Subtract 5 cents and write the equation:
n + d + q = 7
and
.05n + .10d + .25q = 1.70
replace q with (3n)
.05n + .10d + .25(3n) = 1.70
.05n + .10d + .75n = 1.70
.80n + .10d = 1.70
mult by 10
8n + 1d = 17
d = -8n + 17
Assume n = 1, only value that seems reasonable
d = -8 + 17
d = 9 dimes, 1 nickel, then 3 quarters
:
Let's say, 5 pennies, 1 nickel, 9 dimes, 3 quarters
:
.05 + .05 + .90 + .75 = 1.75
:
Hold everything, I forgot about the 12 coins, this is not right
n + d + q = 7
How about 1 nickel 3 dimes, 4 quarters, but that would only give you 1.35
I don't think this can be done with 12 coins if we use pennies.
----------------------------------------------------------------------
I asked my Grandson Donovan about it and he said use a half dollar as one
of the coins,
I came up with
6 nickels, 2 dimes, 3 quarters, 1 half dollar, 12 coins
.30 + .20 + .75 + .50 = 1.75
and
n = 3q
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