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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/647921: In a race of 1000m, Jacqui finishes 110m ahead of Lisa and 180m ahead of Fran. If Lisa and Fran continue at the same rates, how far in front of Fran will Lisa finish? (The answer is not 80m).
1 solutions
Answer 406502 by ankor@dixie-net.com(15656)   on 2012-09-08 22:21:18 (Show Source):
You can put this solution on YOUR website!In a race of 1000m, Jacqui finishes 110m ahead of Lisa and 180m ahead of Fran.
If Lisa and Fran continue at the same rates, how far in front of Fran will Lisa
finish?
:
Assume a time for Jac to run the race, 100 seconds
:
In 100 sec Lisa runs (1000-110) 890 meters
:
Find Lisa's speed: 890/100 = 8.9 m/sec
:
Find how long it takes Lisa to run 1000 m, finish the race
1000/8.9 = 112.36 seconds
:
Find Fran's speed; 1000-180 = 820 m; 820/100 = 8.2 m/sec is Fran's speed
:
Find how far Fran has run when Lisa crossed the finish line in 112.36 sec
8.2*112.36 = 921.35 m
therefore
1000-921.35 = 78.65 m Fran is behind, when Lisa finishes
|
Human-and-algebraic-language/647749: A square and a rectangle have the same area. The square's length is x and width is x for the rectangle's length is 2x-3 and width is x-2. What is the numerical value of the rectangle's perimeter?
1 solutions
Answer 406483 by ankor@dixie-net.com(15656) on 2012-09-08 21:42:30 (Show Source):
You can put this solution on YOUR website!A square and a rectangle have the same area.
The square's length is x and width is x
for the rectangle's length is 2x-3 and width is x-2.
What is the numerical value of the rectangle's perimeter?
:
"A square and a rectangle have the same area."
(2x-3)(x-2) = x^2
2x^2 - 4x - 3x + 6 = x^2
2x^2 - x^2 - 7x + 6 = 0
x^2 - 7x + 6 = 0
Factors to
(x-1)(x-6) = 0
x = 6 is the only reasonable solution
then
2(6)-3 = 9 is the length of the rectangle
and
6 - 2 = 4 is the width
Find the perimeter
2(9) + 2(4) = 26
:
:
Check this by finding the areas
6^2 = 36
9*4 = 36
|
Travel_Word_Problems/647707: a plane flies 400 miles with the wind and 300 miles against the wind in the same length of time. If the speed of the wind is 25 mph, what is the speed of the plane in still air?
1 solutions
Answer 406372 by ankor@dixie-net.com(15656) on 2012-09-08 15:24:00 (Show Source):
You can put this solution on YOUR website!a plane flies 400 miles with the wind and 300 miles against the wind in the
same length of time.
If the speed of the wind is 25 mph, what is the speed of the plane in still air?
:
Let s = speed in still air
then
(s-25) = ground speed against the wind
(s+25) = ground speed with the wind
:
Write a time equation, time = dist/speed
:
Time with the wind = time against the wind
 = 
cross multiply
400(s-25) = 300(s+25)
400s - 10000 = 300s + 7500
400s - 300s = 7500 + 10000
100s = 17500
s = 17500/100
s = 175 mph in still air
:
:
Check this by finding the actual time each way
400/200 = 2 hr
300/150 = 2 hr
|
Mixture_Word_Problems/647653: A mechanic has 343 gallons of gasoline and 18 gallons of oil to make gas/oil mixtures. He wants one mixture to be 6% oil and the other mixture to be 2.5% oil. If he wants to use all of the gas and oil, how many gallons of gas and oil are in each of the resulting mixtures?
1 solutions
Answer 406342 by ankor@dixie-net.com(15656) on 2012-09-08 12:52:59 (Show Source):
You can put this solution on YOUR website!A mechanic has 343 gallons of gasoline and 18 gallons of oil to make gas/oil mixtures.
He wants one mixture to be 6% oil and the other mixture to be 2.5% oil.
If he wants to use all of the gas and oil, how many gallons of gas and oil are
in each of the resulting mixtures?
:
The total amt of the two mixtures: 343+18 = 361
:
Let x = amt of the 6% mixture
then
(361-x) = amt of the 2.5% mixtures
:
Write an amt of oil equation
.06x + .025(361-x) = 18
.06x + 9.025 - .025x = 18
.06x - .025x = 18 - 9.025
.035x = 8.975
x = 9.425/.035
x = 256.4 gal for the 6% mixture
and
361 - 256.4 = 104.6 gal for the 2.5% mixture
:
Find the amt of oil in each
.06(256.4) = 15.4 gal of oil in the 6% mixture
.025(104.6) = 2.6 gal of oil in the 2.5% mixture
--------------------
Check total = 18 gal
:
Find the amt of gas in each mixture
.94(256.4) = 241 gal of gas in the 6% mixture
.975(104.6) = 102 gal of gas in the 2.5% mixture
-----------------
Check gas total: 343 gal
|
Travel_Word_Problems/647535: a nonstop train leaves new york for los angeles traveling at a constant rate of 80 miles per hour. another nonstop train leaves los angeles for new york, at a constant rate of 60 miles per hour both traveling on the same straight track. how far apart are the fronts of the trains in miles 1 hour before they meet?
1 solutions
Answer 406290 by ankor@dixie-net.com(15656) on 2012-09-07 21:12:48 (Show Source):
You can put this solution on YOUR website!a nonstop train leaves new york for los angeles traveling at a constant rate of
80 miles per hour.
another nonstop train leaves los angeles for new york, at a constant rate of 60
miles per hour both traveling on the same straight track.
how far apart are the fronts of the trains in miles 1 hour before they meet?
:
We can use relative speed here, trains going towards each other, their speeds
are additive, 80 + 60 = 140 mph
:
All we have to ask ourselves is how far will be traveled at this speed in 1 hr
Obviously 140 miles apart, one hour before they meet
|
Exponential-and-logarithmic-functions/647427: There are 136 coins in the cash box. There are an equal number of silver dollars and quarters. There are half as many dimes as quarters and one third as many nickels. How much is in the cash box?
1 solutions
Answer 406266 by ankor@dixie-net.com(15656) on 2012-09-07 19:28:14 (Show Source):
You can put this solution on YOUR website!There are 136 coins in the cash box.
There are an equal number of silver dollars and quarters.
There are half as many dimes as quarters and one third as many nickels.
How much is in the cash box?
:
n + d + q + c = 136 (c = no. of silver dollars)
:
"There are an equal number of silver dollars and quarters."
q = c
:
" There are half as many dimes as quarters"
d =  q
or
q = 2d
:
"and one third as many nickels."
d =  n
or
n = 3d
:
n + d + q + c = 136
replace n with 3d, q with 2d, c with 2d
3d + d + 2d + 2d = 136
8d = 136
d = 136/8
d = 17 dimes
then
n = 3(17) = 51 nickels
and
q = 2(17) = 34 quarters
and
c = 2(17) = 34 dollars
:
.05(51) + .10(17) + .25(34) + 1(34) =
2.55 + 1.70 + 8.50 + 34 = $46.75 in the cash box
|
Travel_Word_Problems/647464: Your department sends it's copying to the photocopy center of your company. The center bills your department $.10 per page. You suggest buying a copier for $3000. With your own copier the cost per page would be $.03. The expected life of the copier is four years. How many copies must you make in the four-year period to justify buying the copier?
1 solutions
Answer 406253 by ankor@dixie-net.com(15656) on 2012-09-07 19:04:10 (Show Source):
You can put this solution on YOUR website!Your department sends it's copying to the photocopy center of your company.
The center bills your department $.10 per page.
You suggest buying a copier for $3000.
With your own copier the cost per page would be $.03.
The expected life of the copier is four years.
How many copies must you make in the four-year period to justify buying the copier?
:
let c = no. of copies to break even
:
.10c = .03c + 3000
.10c - .03c = 3000
.07c = 3000
c = 3000/.07
c = 42857.143 ~ 42,858 copies before it will be a better deal
:
:
We can see this:
.10(42858) = $4,285.80 cost with the old copier
.03(42858) + 3000 = $4,285.74 with the new copier, a 6 cent savings!
|
Age_Word_Problems/647285: After 5 years my father would be half the age of my grandfather and my grandfather would be twice the age of mine. Find my grandfathers age after 13 years?
1 solutions
Answer 406222 by ankor@dixie-net.com(15656) on 2012-09-07 18:03:53 (Show Source):
You can put this solution on YOUR website!After 5 years my father would be half the age of my grandfather and my
grandfather would be twice the age of mine.
Find my grandfathers age after 13 years?
:
f + 5 = (g+5)
2(f+5) = g + 5
2f + 10 = g + 5
2f + 10 - 5 = g
g = 2f + 5, grandpa's age now
In 13 yrs
g = 2f + 5 + 13
g = 2f + 18, that's all we do with the given information
:
"my grandfather would be twice the age of mine."does not make sense
|
Age_Word_Problems/647257: jake is now one-quarter of his father age and in 7 years time his age he will be one-third the age of his father. how old is he now ?
1 solutions
Answer 406217 by ankor@dixie-net.com(15656) on 2012-09-07 17:51:16 (Show Source):
You can put this solution on YOUR website!Write an equation for each statement.
:
jake is now one-quarter of his father age
j =  f
or
f = 4j
:
in 7 years time his age he will be one-third the age of his father.
j + 7 = (f+7)
multiply both sides by 3, get rid of the fraction which annoys us.
3(j+7) = f + 7
3j + 21 = f + 7
3j = f + 7 - 21
3j = f - 14
replace f with 4j, (from the 1st statement)
3j = 4j - 14
14 = 4j - 3j
j = 14 yrs old is Jake's present age
:
:
To check this: father's age 4(14) = 56
" in 7 years time his age he will be one-third the age of his father.
14 + 7 = (56+7)
21 = (63)
|
Equations/647345: Cant figure out to solve this equation, I need to solve for the indicated variable, in this case "y"
(y+1)(a-3)=x-2 for y
So far I have this:
ay-3y+a-3=x-2
ay-3y+a-a= x+1-a
ay-3y=x+1-a
Thanks
1 solutions
Answer 406214 by ankor@dixie-net.com(15656) on 2012-09-07 17:37:48 (Show Source):
You can put this solution on YOUR website! Cant figure out to solve this equation, I need to solve for the indicated variable, in this case "y"
(y+1)(a-3)=x-2 for y
So far I have this:
ay-3y+a-3=x-2
ay-3y+a-a= x+1-a
ay-3y=x+1-a
you about got it whipped here, just factor out y on the left
y(a-3) = x + 1 - a
Divide both sides by (a-3)
y = = 
|
Length-and-distance/647130: The ration of length to width of a piece of paper is 15 to 7. A diagonal drawn on the piece of paper has a length of 0.0662dam. What are the dimensions of the page in cm. Tried using the pythagorus theory, but stuck because of the unknown length and width.
1 solutions
Answer 406211 by ankor@dixie-net.com(15656) on 2012-09-07 17:27:29 (Show Source):
You can put this solution on YOUR website!The ratio of length to width of a piece of paper is 15 to 7.
A diagonal drawn on the piece of paper has a length of 0.0662dam.
What are the dimensions of the page in cm.
:
Let x = the multiplier
then
15x = the actual length
and
7x = actual width
:
Assume .0662dam means .0662 decameters (10 meters)
.0662 decameters = .662 meters
.662 * 100 = 66.2 cm
:
Using a^2 + b^2 = c^2, where
a = 15x
b = 7x
c = 66.2
:
(15x)^2 + (7x)^2 = 66.2^2
225x^2 + 49x^2 = 4382.44
274x^2 = 4382.44
x^2 = 4382.44/274
x^2 ~ 16
x = 
x = 4 is the multiplier
:
15*4 = 60 cm is the length
and
7*4 = 28 cm is the width
:
:
Check this on a calc: enter:  results 62.2
|
Linear_Equations_And_Systems_Word_Problems/647079: A college charters a bus for $1700 to take a group to a museum. When six more students join the trip, the cost per student drops by $7.50. How many students are in the original group?
1 solutions
Answer 406184 by ankor@dixie-net.com(15656) on 2012-09-07 14:55:54 (Show Source):
You can put this solution on YOUR website!A college charters a bus for $1700 to take a group to a museum.
When six more students join the trip, the cost per student drops by $7.50.
How many students are in the original group?
:
Let n = number to students in the original group
then
 = the original cost
:
(n+6) = no. when six more students join
and
 = the cost when six more join
:
Original cost - six more cost = 7.50
- = 7.50
:
multiply by n(n+6), results:
1700(n+6) - 1700n = 7.5n(n+6)
1700n + 10200 - 1700n = 7.5n^2 + 45n
:
Combine as a quadratic equation
7.5n^2 + 45n - 10200 = 0
:
simplify, divide thru by 7.5
n^2 + 6n - 1360 = 0
:
You can use the quadratic formula, but this will factor to:
(n+40)(n-34) = 0
:
the positive solution
n = 34 original students
:
:
Check this, find the actual cost for each scenario
1700/34 = $50.00
1700/40 = $42.50, a $7.50 difference
|
Travel_Word_Problems/647172: A train leaves NYC for Washington DC traveling at 90 mph. At the SAME TIME, a train leaves Washington DC for NYC traveling at 95 mph. If NYC and Washington DC are 462.5 miles apart, how long will it take before the two trains meet?
*I do believe that "how long will it take" refers to the distance in miles since the problem doesn't involve time.
Will the question have two answers since there are two starting points?
Thank you for your help :D
1 solutions
Answer 406019 by ankor@dixie-net.com(15656) on 2012-09-06 21:56:21 (Show Source):
You can put this solution on YOUR website!A train leaves NYC for Washington DC traveling at 90 mph.
At the SAME TIME, a train leaves Washington DC for NYC traveling at 95 mph.
If NYC and Washington DC are 462.5 miles apart, how long will it take
before the two trains meet?
:
let t = traveling time in hr until they meet
:
When they meet the sum of the two trains traveling distances will equal 462.5
Write a distance equation; dist = speed * time
:
90t + 95t = 462.5
add like terms
185t = 462.5
divide both sides by 185
t = 
t = 2.5 hrs for them to meet
:
:
You can check this by finding the actual distance each train traveled
2.5(90) = 225 mi
2.5(95) = 237.5 mi
--------------------
total dist: 462.5, the dist from N.Y to D.C.
|
Age_Word_Problems/646951: Karen is twice as old as Maria. Karen is also three years older than Maria. How old is Maria?
1 solutions
Answer 406011 by ankor@dixie-net.com(15656) on 2012-09-06 21:36:52 (Show Source):
You can put this solution on YOUR website!Write an equation for each statement
:
Karen is twice as old as Maria.
k = 2m
Karen is also three years older than Maria.
k = m + 3
Replace k with 2m (from the 1st statement)
2m = m + 3
2m - m = 3
m = 3 yrs is Maria's age
|
logarithm/646647: The half-life of radioactive strontium-90 is approximately 29 years. In 1964, radioactive strontium-90 was released into the atmosphere during testing of nuclear weapons, and was absorbed into people's bones. How many years (since 1964) does it take until only 9 percent of the original amount absorbed remains?
1 solutions
Answer 406008 by ankor@dixie-net.com(15656) on 2012-09-06 21:23:45 (Show Source):
You can put this solution on YOUR website!The half-life of radioactive strontium-90 is approximately 29 years.
In 1964, radioactive strontium-90 was released into the atmosphere during
testing of nuclear weapons, and was absorbed into people's bones.
How many years (since 1964) does it take until only 9 percent of the
original amount absorbed remains?
:
The radio-active decay formula: A = Ao*2^(-t/h), where
A = resulting amt after t time
Ao = initial amt (t=0)
t = time of decay
h = half-life of substance
:
Let initial amt = 100 then resulting amt = 9
100*2^(-t/29) = 9
divide both sides by 100
2^(-t/29) = .09
using nat logs, the log equiv of exponents
 *ln(2) = ln(.09)
= 
= -3.47393
t = -29 * -3.47393
t = 100.744 yrs, plus 1964 = 2065 for bones to be reduced to 9%
:
:
:
That seemed like a long time, checked on a calc:
enter 100*2^(-100.744/29) results: 9.000
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Distributive-associative-commutative-properties/646970: How do I write an equation that models how old in years a 43, 55, and 15 year old will be, when our ages add up to 150 years old.
1 solutions
Answer 405998 by ankor@dixie-net.com(15656) on 2012-09-06 20:17:19 (Show Source):
You can put this solution on YOUR website!How do I write an equation that models how old in years a 43, 55, and 15
year old will be, when our ages add up to 150 years old.
:
Let y = no. yrs for this to be true
:
Each will age y yrs, therefore
(y+43) + (y+55) + (y+15) = 150
3y + 113 = 150
3y = 150 - 113
3y = 37
y = 37/3
y = 12 yrs
:
Add 12 to each ones age
55 + 67 + 27 = 150
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Travel_Word_Problems/646691: darcy and ian live 24km apart. One day, they agreed to ride a bicycle and meet in a place between the towns where they live. Darcy travelled with a speed of 20kph while Ian 12kph. If they left their respective houses at 9:30, at what time did they meet?
1 solutions
Answer 405989 by ankor@dixie-net.com(15656) on 2012-09-06 18:47:22 (Show Source):
You can put this solution on YOUR website!darcy and ian live 24km apart.
One day, they agreed to ride a bicycle and meet in a place between the
towns where they live.
Darcy traveled with a speed of 20kph while Ian 12kph.
If they left their respective houses at 9:30, at what time did they meet?
:
Let t = the travel time of the two bikes
:
When they meet, the sum of their travel distances will be 24 km
Write a distance equation; dist = speed * time
:
20t + 12t = 24
32t = 24
t = 24/32 = 3/4 hr which is 45 minutes
:
9:30 + :45 = 10:15 when they meet
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Quadratic_Equations/646727: Professor I'm sorry to keep bothering you but I'm really desperate with this problem. I have no idea how to solve it at all. My worksheet says solve the equation and I think it's quadratic. Please help me with this.
(3/3x)-(1/x+1)= 1
And here are my choices (A)0 (B)-1+the square root of 5 over 2 (C)-3+ the square root of 5 over 2 or (D) 1+ square root of 5 ovr 2
I tried finding the common denominator, as a result I got 0 but I'm not sure if that's correct. Thank you so much for your time. I highly appreciate this.
1 solutions
Answer 405973 by ankor@dixie-net.com(15656) on 2012-09-06 16:53:27 (Show Source):
You can put this solution on YOUR website!Assuming this is the equation
 = 1
just cancel the 3 leaving
 = 1
multiply both sides by x(x+1), results:
(x+1) - x = x(x+1)
x -x + 1 = x^2 + x
A quadratic equation
x^2 + x - 1 = 0
use the quadratic formula; a=1; b=1; c=-1
:
Two solutions
and
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Trigonometry-basics/646857: A plane rises from take-off and flies at an angle of 10 degrees with the horizontal runway. When it has gained 500 feet of altitude, find the distance, to the nearest foot, the plane has flown.
1 solutions
Answer 405965 by ankor@dixie-net.com(15656) on 2012-09-06 15:50:54 (Show Source):
You can put this solution on YOUR website!A plane rises from take-off and flies at an angle of 10 degrees with the
horizontal runway.
When it has gained 500 feet of altitude, find the distance, to the nearest
foot, the plane has flown.
:
This can be solved using the sine of 10 degrees,
side opposite is 500 ft
hypotenuse = slant distance (s) flown by the plane
sin(10) = 
s = 
s = 2,879 ft flown by the plane to reach 500 ft alt
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Travel_Word_Problems/646760: two cars, which are 424 miles apart and whose speeds differ by 8 miles per hour, are moving toward each other. If they meet in 4 hours, find the speed of each car.
1 solutions
Answer 405960 by ankor@dixie-net.com(15656) on 2012-09-06 15:41:37 (Show Source):
You can put this solution on YOUR website! two cars, which are 424 miles apart and whose speeds differ by 8 miles per
hour, are moving toward each other.
If they meet in 4 hours, find the speed of each car.
:
Let s = the speed of the slower car
then
(s+8) = speed of the faster
:
Write a distance equation: dist = time * speed
4s + 4(s+8) = 424
4s + 4s + 32 = 242
8s = 424 - 32
8s = 392
s = 392/8
s = 49 mph is the slower car
then
49+8 = 57 mph is the faster car
:
:
Check this; find the dist traveled by each car
4(49) = 196 mi
4(57) = 228 mi
----------------
total d: 424 mi
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Travel_Word_Problems/646572: A search plane has a cruising speed of 250 mph and carries enough fuel for at most 5 hours of flying. If there is a wind that averages 30 mph and the direction of the search is with the wind one way and against it the other, how far can the search team travel before it has to turn back?
1 solutions
Answer 405910 by ankor@dixie-net.com(15656) on 2012-09-06 09:10:30 (Show Source):
You can put this solution on YOUR website!A search plane has a cruising speed of 250 mph and carries enough fuel
for at most 5 hours of flying.
If there is a wind that averages 30 mph and the direction of the search
is with the wind one way and against it the other, how far can the search
team travel before it has to turn back?
:
This is a "point of no return" problem
:
Let d = the one-way distance to the point of no return
:
250 - 30 = 220 mph ground speed against the wind
250 + 30 = 280 mph ground speed with the wind
:
Write a time equation; Time = dist/speed
:
outbound time + inbound time = 5 hrs
 +  = 5
find the least common multiple, prime factor
22: 2, 11
28: 2, 2, 7
2*2*7*11*10 = 3080
Multiply equation by 3080
3080* + 3080* = 3080*5
Cancel the denominators
14d + 11d = 15400
d = 15400/25
d = 616 miles to turn back point
:
:
Check this by finding the actual time each way
616/220 = 2.8 hrs outbound
616/280 = 2.2 hrs to return
-------------------
total time: 5 hrs
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Geometry_Word_Problems/646016: It took a crew 6 h 24 min to row 6 km upstream and back again. If the rate of flow of the stream was 7 km/h, what was the rowing speed of the crew in still water?
1 solutions
Answer 405881 by ankor@dixie-net.com(15656) on 2012-09-05 21:49:29 (Show Source):
You can put this solution on YOUR website! It took a crew 6 h 24 min to row 6 km upstream and back again.
If the rate of flow of the stream was 7 km/h, what was the rowing speed
of the crew in still water?
:
Change 6 hrs, 24 min to hrs, 6 + 24/60 = 6.4 hrs
:
Let s = rowing speed in still water
then
(s-7) = effective speed upstream
and
(s+7) = effective speed downstream
:
Write time equation, time = dist/speed
:
 +  = 6.4
multiply by (s-7)(s+7), obtain a quadratic equation and solve
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Mixture_Word_Problems/646331: Please help me solve for x in the following equation: 1/4x + 1/6 = 1/3(x-4) I do know that x= 18 but I am unaware of how to receive that answer.
1 solutions
Answer 405880 by ankor@dixie-net.com(15656) on 2012-09-05 21:38:19 (Show Source):
You can put this solution on YOUR website!Assume the problem is:
x +  = (x-4)
get rid of the denominators, least common multiple is 12, mult by 12
12* x + 12* = 12* (x-4)
cancel out the denominators and you have
3x + 2 = 4(x-4)
3x + 2 = 4x - 16
2 + 16 = 4x - 3x
18 = x
:
How about this? Did this make sense to you?
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Age_Word_Problems/646036: harry is x years old, his brother is two times older and his sister is 5 years younger than harry.
A equation to show this situation?.
Solve the equation to find their ages.
1 solutions
Answer 405879 by ankor@dixie-net.com(15656) on 2012-09-05 21:29:49 (Show Source):
You can put this solution on YOUR website!harry is x years old, his brother is two times older and his sister
is 5 years younger than harry.
A equation to show this situation?
:
2x = brothers age
(x-5) = sister's age
;
Solve the equation to find their ages.
not enough info here to solve this
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