Question 1130236
.


Starting from November 2025 and during December 2025 I worked on checking solutions 
provided by @mananth at this forum www.algebra.com .


For now, Jan.06, 2026, I reviewed/checked about  2*17*31 = 1054 problems, solved
by @mananth at this web-site (problems from  2390..9419  to  10320..10349  inclusively
of the list  https://www.algebra.com/tutors/your-answers.mpl?userid=mananth ).


Of them, I found about 99 problems solved incorrectly. 
Below is the list of these problems, solved incorrectly.
For each of these problems, my correct solution is placed at the same spot/link.


I started this my checking job from some of the problems, and after checking approximately 70 problems,
I started noticing the repeating patterns in problems and in their solutions.
Quite often, these solutions were incorrect, and the errors were of the kind a live person would not 
make them. It led me to the idea that the solution were actually produced not by a living person, 
but by a computer code, instead. So, it was a very early version of the Artificial Intelligence.


After getting this observation, two ideas led me.


First idea was, of course, to clean this forum from erroneous solutions.
Second idea was to learn how far this artificial intelligence may lead in producing wrong and right solution.
So, this file is my report on this issue.


I collected here only wrong solutions (wrong from a Math point of view).
There were also cases, when the solutions were led to correct answers, but were wrong
from an educative/pedagogical point of view. Then suggestions "wrong/correct" become more individualized/personalized,
and I did not include such cases in this my file. So, only incorrect solutions are collected/listed here.


From about 1000 reviewed problems, the number of incorrectly solved is about 100 (for now).
In other words, about 10% of all problems were solved incorrectly by @mananth (by his version of AI).


<pre>
457475     (1)
How do I solve and algebra problem with a squared variable? 25=16-Tsquared

https://www.algebra.com/algebra/homework/Square-cubic-other-roots/Square-cubic-other-roots.faq.question.457475.html


457528
Can  someone help me solve the solutin of the system using the elemination method?
5x + 2y = -11
7x - 3y = 13

https://www.algebra.com/algebra/homework/coordinate/Linear-systems.faq.question.457528.html


457531
Linear-systems/457531: Can someone help me solve the solution of the system using the elemination method?
0.3x - 0.2y = 4
0.5x + 0.5y = 45/23

https://www.algebra.com/algebra/homework/coordinate/Linear-systems.faq.question.457531.html


457527
Can someone help me solve the solution of the system by using the elimination method to find the solution?
x + 5y = 20
-x + 8 = 19

https://www.algebra.com/algebra/homework/coordinate/Linear-systems.faq.question.457527.html


455657
Using the Point-Slope form to write equations
m=3/4, (2,-6)
y--6=3/4(x--2)
How do I solve this problem?

https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.455657.html


454369
Write an equation of the line containing the given point and parallel to the given line. 
Express your answer in the form y=mx+b
(-6,7); 2x=9y+8

https://www.algebra.com/algebra/homework/equations/Equations.faq.question.454369.html


453363
solve {{{49a^2-56a+16=0}}} 
please justify your answer thank you

https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.453363.html


454327
Solve the linear system by using substitution. 3x+2y=5, 5x-9y=-4

https://www.algebra.com/algebra/homework/Expressions-with-variables/Expressions-with-variables.faq.question.454327.html


453794
solve by completing the square.
x^2+4x-12=0

https://www.algebra.com/algebra/homework/complex/Complex_Numbers.faq.question.453794.html


454259     (10)
Use substitution method to determine whether the system of linear equations has no solution, one solution,or many solutions
2x - y = 8
x + 4y = 13

https://www.algebra.com/algebra/homework/coordinate/Linear-systems.faq.question.454259.html


454258
solve using substitution method
x - 5y = 17
-5x - 6y = 8

https://www.algebra.com/algebra/homework/coordinate/Linear-systems.faq.question.454258.html


454379
Find an eaution of the line containing the given pair of points.
(-7,-9) and (-4,-8)

https://www.algebra.com/algebra/homework/equations/Equations.faq.question.454379.html


453353
what is the slope-intercept of 2x-7y=-24 passing through (9,11)

https://www.algebra.com/algebra/homework/Linear-equations/Linear-equations.faq.question.453353.html


452963
I am having a problem factoring this one 14a^(2)-45a-14

https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.452963.html


451898
How do I set this problem up:
If a farmer stand owner mixes apple juice and cranberry juice, how much should he charge if he mixes 8L 
of apple juice selling for 45 cents a liter with 10L of cranberrt juice sellling for $1.08 a liter.

https://www.algebra.com/algebra/homework/Expressions-with-variables/Expressions-with-variables.faq.question.451898.html


451984
i am having troubles with solving the systems of equations in substitution. 
how do you solve the equation x-2y=0 and 4x-3y=15 in ordered pair form, (x,y)?

https://www.algebra.com/algebra/homework/Systems-of-equations/Systems-of-equations.faq.question.451984.html


452157
bayside insurance offers two health plans. 
under plan a, giselle would have to pay the first $120 of her medical bills, plus 30% of the rest. 
under the plan b, giselle would pay the first $160, but only 20% of the rest. 
for what amount of medical bills will plan b save giselle money? assume she has over $160 in bills 
giselle would save with plan b if she had more than $ in bills.

https://www.algebra.com/algebra/homework/coordinate/word/Linear_Equations_And_Systems_Word_Problems.faq.question.452157.html


453010
joanne mows the front yard in 40 min, while hope can mow the same yard in 50 min. how long would it take them, working together with two mowers, to mow the yard?

https://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Rate-of-work-word-problems.faq.question.453010.html


449831
a  circle has a diameter with endpoints (5,-2) and (-13,-6) what are the coordinates of the center of the circle

https://www.algebra.com/algebra/homework/word/geometry/Geometry_Word_Problems.faq.question.449831.html


448805      (20)
graph the line that goes through point (3,8) and is parallel to the line whose equation is 6y-10x=30

https://www.algebra.com/algebra/homework/Linear-equations/Linear-equations.faq.question.448805.html


449484
Solve by the elimination method.
0.3x-0.2y=4
0.2x+0.5y=-75/17

https://www.algebra.com/algebra/homework/Expressions-with-variables/Expressions-with-variables.faq.question.449484.html


447774
how to simplify sqrt (12ab^3c^2)

https://www.algebra.com/algebra/homework/Expressions-with-variables/Expressions-with-variables.faq.question.447774.html


448811
at the beginning of a walk Roberto and Juanita are 7.7 miles apart. If they leave at the same time and walk 
in the same direction, Roberto overtakes Juanita in 11 hours. If they walk towards each other, they meet 
in 1 hour what are their speeds?

https://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.448811.html


449124
The radiator in Natalie's car contains 6.3 L of antifreeze and water. This mixture is 30% antifreeze. 
How much of this mixture should she drain and replace with pure antifreeze so that there will be 
a mixture of 50% antifreeze?

https://www.algebra.com/algebra/homework/word/mixtures/Mixture_Word_Problems.faq.question.449124.html


448811
At the beginning of a walk Roberto and Juanita are 7.7 miles apart. If they leave at the same time and walk 
in the same direction, Roberto overtakes Juanita in 11 hours. If they walk towards each other, they meet 
in 1 hour what are their speeds?

https://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.448811.html


449124
The radiator in Natalie's car contains 6.3 L of antifreeze and water. This mixture is 30% antifreeze.
How much of this mixture should she drain and replace with pure antifreeze so that there will be 
a mixture of 50% antifreeze?

https://www.algebra.com/algebra/homework/word/mixtures/Mixture_Word_Problems.faq.question.449124.html


448767
Write an equation of the line containing the given point and parallel to the given line. 
Express your answer in the form y=mx+b.
(8,9); x+7y=2

https://www.algebra.com/algebra/homework/Linear-equations/Linear-equations.faq.question.448767.html


447905
substitution
a - 4b = 2
2a - 5b = 1
with steps too

https://www.algebra.com/algebra/homework/coordinate/Linear-systems.faq.question.447905.html


448337
What is the answer to this equation 2x/5 = 4+2/3 ? If Not the answer how do i solve this equation?

https://www.algebra.com/algebra/homework/equations/Equations.faq.question.448337.html


448309    (30)
A milk tank can be filled by pip A in 6 hours, by pipe B in 8 hours and by pipe C in 12 hours. 
how long will it take all three pipes working together to fill the tank?

https://www.algebra.com/algebra/homework/word/mixtures/Mixture_Word_Problems.faq.question.448309.html


448368
Jim opens a savings account with a deposit of $10,000. If the account has an annual interest rate of 6%, 
compounded quarterly, how much is in the account after one year.
Can you show me steps on how to work this problem. It's been years since I had algebra. Thank you so much.

https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.448368.html


448477
Find the slope of the line that contains the points 9,8 and -2,1

https://www.algebra.com/algebra/homework/Linear-equations/Linear-equations.faq.question.448477.html


447396
I need help writing the slope-intercept equation for the line that passes through (-3, -15) and is perpendicular 
to -6x + 8y = 3. Thank you.

https://www.algebra.com/algebra/homework/equations/Equations.faq.question.447396.html


447773
A  circular swimming pool has a diameter of 8 M and a depth of 2 m. what is the volume of the swimming pool?

https://www.algebra.com/algebra/homework/Volume/Volume.faq.question.447773.html


446417
A pump can empty a swimming pool at a rate of 35 liters per minute. At that rate, how many days will it take 
to empty a pool of 10,000 gallons?

https://www.algebra.com/algebra/homework/conversion/Reduction-of-unit-multipliers.faq.question.446417.html


446771
(y^2-4/y+3)=2-(y-2/y+3)

https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.446771.html


446848
A new machine can make 10,000 aluminum cans three times faster than an older machine. with both machines working, 
10,000 cans be made in 9h. how long would it take the new machine, working alone, to make the 10,000 cans?

https://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Rate-of-work-word-problems.faq.question.446848.html


446858
Find  the slope of AC and BD. Decide whether AC is perpendicular to BD.
A(-1,-2) B(-3,2) C(0,1) D(3,0)

https://www.algebra.com/algebra/homework/Points-lines-and-rays/Points-lines-and-rays.faq.question.446858.html


446364
Palmer's average running speed is 3 Kilometers per hour faster than his walking speed. If Palmer can run 
around a 20-Kilometer course in 2 hours, how many hourse would it take her Palmer to walk the same course?
I NEED TO SEE THE WORK ON HOW YOU GOT THE ANSWER!!

https://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.446364.html


446358    (40)
One  person can do a certain job in six days, a second person can do the same job in two days, and a third person 
can do this job in three days. How many days will they take to do the job together?

https://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Rate-of-work-word-problems.faq.question.446358.html


445280
what is the surface area of 3 ft by 3 ft by 4 ft

https://www.algebra.com/algebra/homework/Surface-area/Surface-area.faq.question.445280.html


445280
what is the surface area of 3 ft by 3 ft by 4 ft

https://www.algebra.com/algebra/homework/Surface-area/Surface-area.faq.question.445280.html


445381
What are the solutions to
6x+3y+z=19
x-3y+2z=21
17x-2y+3z=86

https://www.algebra.com/algebra/college/linear/Linear_Algebra.faq.question.445381.html


445895
7 audio cassettes and 3 video cassettes cost rs 1110,while 5 audio cassettes and 4 video cassettes cost rs 1350 
find the cost of an audio cassette and a video cassette

https://www.algebra.com/algebra/homework/coordinate/word/Linear_Equations_And_Systems_Word_Problems.faq.question.445895.html


443624
Write  the slope-intercept equation for the line that passes through (-7, 6) and is perpendicular to -7x + 9y = -2 
Please show all of your work.

https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Quadratic-relations-and-conic-sections.faq.question.443624.html


443021
Bayside insurance offers two health plans. 
Under plan A, Giselle would have to pay the first $100 of her medical bills plus 25% of the rest. 
Under plan B, Giselle would pay the first $160, but only 20% of the rest.
For what amount of medical bills will plan B save Giselle money? assume she has over $160 in bills.
Giselle would save with plan B if she had more than what in medical bills?

https://www.algebra.com/algebra/homework/percentage/percentage.faq.question.443021.html


444160
My problem is this: A truck enters a highway driving 60mph. A car enters the highway at the same place 12 minutes later and drives 67mph in the same direction. How long before the car passes the truck?
I have My Math Lab on coursecompass.com and it kind of explains the solving process but I seem to get lost at the end.
I know that the problem needs to be set up with d(t)=60(t + 10) and d(c)=67t but after that I get lost. Please help.

https://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.444160.html


444146 
6x - y = 39
6x + 7y=33

https://www.algebra.com/algebra/homework/Expressions-with-variables/Expressions-with-variables.faq.question.444146.html


444555
Solve. Please show the algebraic inequality you used and show all of your work.
A furniture rental company charges a base rate plus a rate per day for an office furniture set. 
There are two available plans. The Super Saver Plan charges $100 + $5 per day. 
The Best Deal Plan charges $150 + $3 per day. 
How many days make the Super Saver Plan more expensive than the Best Deal Plan?

https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.444555.html


444813    (50)
I need to find the equation of the line containing (-2, -7) and (-5, -8)

https://www.algebra.com/algebra/homework/Linear-equations/Linear-equations.faq.question.444813.html


440722
Could someone please help me to graph the line containing the given pair of points and find the slope?
(6,3), (-5,-2)

https://www.algebra.com/algebra/homework/Graphs/Graphs.faq.question.440722.html


441209
Bayside insurance offers two health plans. 
Under plan A, Giselle would have to pay the first $160 of her medical bills, plus 25% of the rest. 
Under plan B, Giselle would pay the first $240, but only 20% of the rest, 
for what amount of medial bills will plan B save Giselle money? Assume she has over $240 in bills

https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.441209.html


442300
A boat traveled 210 miles downstream and back. The trip downstream took 10 hours. The trip back
took 70 hours. What is the speed of the boat in still water? What is the speed of the current?

https://www.algebra.com/algebra/homework/word/numbers/Numbers_Word_Problems.faq.question.442300.html


442367
20000$ is split into two investments one paying 5% and the other paying 6.5% to the nearest cent how much 
should be invested in each so the yearly interest from the 5% investment is double the interest from 6.5% investment

https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.442367.html


439388 
Bayside insurance offers two health plans. 
Under plan a, Giselle would have to pay the first $70 of her medical bills, plus 35% of the rest. 
Under plan b, Giselle would have to pay the first $230 and 30% for of the rest. 
For what amount of medical bills will plan b save Giselle money?

https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.439388.html


437577
Flying against a headwind, a plane covers 900 miles in 2 hours. The return trip with a tailwind only takes 
an hour and a half. Find the speed of the wind, and the speed of the plane within the air mass.

https://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.437577.html


437560
Sarah  hikes at 4 kilometers per hour from one end of a trail that is 34 km long. Amanda begins 1 hr laater 
at the other end. Walks toward sarah at 6 k/m. How long will it take for them to pass each other

https://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.437560.html


439419   
A swimming pool holds 540,000 liters of water. THe pool has two drainage pipes. When the pool is completely full, 
the first pipe alone can empty it in 180 min, and the second pipe alone can empty it in 120 min. When both pipes 
are draining together, how long does it take them to empty the pool?

https://www.algebra.com/algebra/homework/coordinate/word/Linear_Equations_And_Systems_Word_Problems.faq.question.439419.html


436823
How long does it take $875 to double if it is invested at 8% compounded monthly?

https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.436823.html


436704    (60) 
A plane flies 1500 miles against the wind in 3 hours and 45 minutes. The return trip with the wind takes 3 hours. 
Assume that the wind speed stays constant. Find the speed of the wind and the speed of the airplane with no wind.

https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.436704.html


437121
Sue can shovel snow from her driveway in 30 mins. Jim can do the same job in 35 mins. 
how long would it take Sue and Jim to shovel the driveway if they worked together?

https://www.algebra.com/algebra/homework/playground/test.faq.question.437121.html


436132
It takes 60 minutes to fill a pond with water alone.
It takes 80 minutes to drain a pond of water alone.
How long will it take to fill the pond while it is being drained at the same time?

https://www.algebra.com/algebra/homework/Expressions-with-variables/Expressions-with-variables.faq.question.436132.html


436154
A holding pen for cattle must be square and have a diagonal length of 140 meters.
Find the length of a side of the pen?
Find the area of the pen?

https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.436154.html


434074
The sum of the present ages of john and his father is 89 years. After 11 years the age of father will be 
twice the age of john at that time, find their present ages.

https://www.algebra.com/algebra/homework/word/age/Age_Word_Problems.faq.question.434074.html


434148
John and Brian leave Williston at the same time. John drives north and Brian drives east. John's average speed 
is 10 miles per hour slower than Brian's. At the end of one hour they are 50 miles apart. Find Brian's average speed.

https://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.434148.html


434949
What will be the future value in a year if $600 is invested at a rate of 15% compounded quarterly

https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.434949.html


434946 
Bertha has 33 coins in her pocket totaling $5.25. If she only has nickles and quarters, how many of each type of coin does she have

https://www.algebra.com/algebra/homework/word/coins/Word_Problems_With_Coins.faq.question.434946.html


435031
$2000 total deposit with 2 savings accounts. One pays interest rate of 6%the other at rate of 8% 
if a total earned interest is $144 how much is each deposit

https://www.algebra.com/algebra/homework/Graphs/Graphs.faq.question.435031.html


432879
final amount of the investment if $8000 invested at 6% compounded quarterly for 6 years

https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.432879.html


433975    (70)
A long distance runner started on a course running at an average speed of 6 mph. one-half hour later, 
a second runner began the same course at an average speed of 7mph. How long after the second runner 
started did the second runner overtake the first runner?

https://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.433975.html


433981
10 gallons of a 15.0% alcohol solution are to be mixed with a 28.0% alcohol solution to make a 20.0% alcohol solution. 
How many gallons of a 28.0% alcohol must be used? How many gallons of a 20.0% alcohol solution are made?

https://www.algebra.com/algebra/homework/word/mixtures/Mixture_Word_Problems.faq.question.433981.html


434087
Solve this equation by sustitution
x=8-4y
2x-3y=13

https://www.algebra.com/algebra/homework/coordinate/Linear-systems.faq.question.434087.html


431703
One plane traveled 800 miles in the same time a second plane traveled 1,000 miles. The rate of the second plane was 
50 mi/h faster than the rate of the first plane. How fast did each plane fly?

https://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.431703.html


430695 
write and equation of the line containing the points (3,-1) and is parallel to 8x-7y=9

https://www.algebra.com/algebra/homework/Linear-equations/Linear-equations.faq.question.430695.html


430837 
x^2+8x+15>=0

https://www.algebra.com/algebra/homework/Graphs/Graphs.faq.question.430837.html


431238
which equation represents a line that passes through the points (2,3) and (-1, -3)?

https://www.algebra.com/algebra/homework/Linear-equations/Linear-equations.faq.question.431238.html


431339
how do u find the midpoint of the line segment of (10,-10),(9,-9)?

https://www.algebra.com/algebra/homework/Linear-equations/Linear-equations.faq.question.431339.html


430008
A developer needs $80,000 to buy land. He is able to borrow the money at 7% compounded quarterly. 
How much interest will be paid on the loan if it is paid off in 5 years? (To the nearest dollar, do not include the $)

https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.430008.html


428476 
Flying from Tokyo to London is approximately 6175 miles. On the way to London from Tokyo(against the wind) the flight 
took 13 hours. the return flight (with the wind) took 9.88 hours. Find the speed of the plane in still air and the 
speed of the wind current.

https://www.algebra.com/algebra/homework/Linear-equations/Linear-equations.faq.question.428476.html


430019    (80)
Could anyone help me with the following?
What would be the semiannual interest payment on a $24,000 Proctor and Gamble 10-year bond at 6.875%? (round to the nearest dollar)
and...
What would be total amount of interest earned on a $24,000 Proctor and Gamble 10-year bond at 6.875% over the entire life of the bond?
Thank you in advance!!

https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.430019.html


430373
Can anyone help me with the following?
If you deposit $2500 in an account paying 4.5% interest compounded semiannually, how much will be in the account after 8 years? (Round to the nearest cent)
Thank you!!

https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.430373.html


418623
If the sum of the lengths of the edges of a cube is 48 inches, the volume of the cube is?

https://www.algebra.com/algebra/homework/word/geometry/Geometry_Word_Problems.faq.question.418623.html


419077
Dave Horn invested half of his money at 5%, one-third of his money at4%, and the rest at 3.5%. 
If his total annual investment income is $530, how much had he invested?

https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.419077.html


419129 
A glue company needs to make some glue tat it can sell at $120 per barrel. It wants to use 150 barrels of glue 
worth $100 per barrel, along with glue worth $150 per barrel and glue worth $190 per barrel. It must use 
the same number of barrels of $150 and $190 glue. How much of the $150 and $190 glue will be needed?
How many Barrels of $120 glue will be produced?

https://www.algebra.com/algebra/homework/coordinate/word/Linear_Equations_And_Systems_Word_Problems.faq.question.419129.html


419040 
The current of a river is 2 miles per hour. A boat travels to a point 8 miles upstream and back again in 3 hours.
What is the speed of the boat in still water?

https://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.419040.html


419037
The speed of a boat in still water is 5 miles per hour. If the boat travels 3 miles downstream in the same amount 
of time it takes to travel 1.5 miles upstream, what is the speed of the current?

https://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.419037.html


419685
Hi tutor, i do not get this question what so ever. It his a problem solving, algebraic question. I really need help. 
It would be greatly appreciated, thank you so much, may god bless you. Q : 500 tickets for a football game were sold 
and the total receipts were $105. Some of the tickets sold for $15 and the rest sold for 25cents. Find the number 
of each sold. ( i am required too provide a equation/formula , write a table i already have that set up : i have it as ticket 1 & ticket two & value, number and amount. & i also would greatly appreciate if you show the work as too how you got the answers, so i can learn from it. Thank you so much.

https://www.algebra.com/algebra/homework/word/coins/Word_Problems_With_Coins.faq.question.419685.html


420019
what is the slope-intercept form that contains the points (3,7) and (3,5)

https://www.algebra.com/algebra/homework/Linear-equations/Linear-equations.faq.question.420019.html


420867 
If I have a 20 qt radiator containing a 80% antifreeze solution. How much of the solution should I drain 
and replace with pure water to get a solution that is 50% antifreeze?

https://www.algebra.com/algebra/homework/word/evaluation/Evaluation_Word_Problems.faq.question.420867.html


421830     (90)
-4x-2y=-8 y=-2x+4

algebra.com/algebra/homework/Expressions-with-variables/Expressions-with-variables.faq.question.421830.html


421840
Solve each system of equations using the substitution method.
4x - y = 32y = -2 x + 70

https://www.algebra.com/algebra/homework/Matrices-and-determiminant/Matrices-and-determiminant.faq.question.421840.html


422281
I'm trying to solve when a man knows he has lost 12.4 percent of his weight, and now weighs 249.6. 
What was his starting weight?

https://www.algebra.com/algebra/homework/proportions/Proportions.faq.question.422281.html


423336 
A liter of orange fruit drink contains 22% orange juice. How many millimeters of orange juice must be added 
to produce a mixture containing 50% orange juice?

https://www.algebra.com/algebra/homework/percentage/percentage.faq.question.423336.html


423677
what is the equation of a line that passes through (-5, 1) and is parallel to y = x + 4 ?
please show steps to help me understand

https://www.algebra.com/algebra/homework/Linear-equations/Linear-equations.faq.question.423677.html


423206 
solving linear systems using substitution, what is
4x-7y=10
y=x-7

https://www.algebra.com/algebra/homework/Systems-of-equations/Systems-of-equations.faq.question.423206.html


423288
An airplane flew for 3 hours with a tail wind of 18 kilometers per hour. The return flight against the wind took 4 hours. Find the rate of the plane in still air.

https://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.423288.html


424727 
Children's tickets to a movie cost $4. Adult tickets cost $7. If 275 tickets were sold for a total cost of $1174, 
how many of each type were sold?

https://www.algebra.com/algebra/homework/coordinate/word/Linear_Equations_And_Systems_Word_Problems.faq.question.424727.html


426400
It takes a freight train 3 hours more to travel 280 miles than it takes an express train to travel 200 miles. 
The rate of the express is 10 miles per hour faster the the rate of the freight train. Fine the rates of both trains.

https://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.426400.html


425874    (99)
a lion devours a sheep in 4 hours. a leopard devours a sheep in 5 hours. a bear devours a sheep in 6 hours. 
how long will it take the three animals eating simultaneously to consume a single sheep?

https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.425874.html
</pre>


/\/\/\/\/\/\/\/\/\/\/\/



You may ask me - ok, @mananth is a computer code, or AI - what does it change ?


Ok, below are my thoughts and my suggestions about it.



<pre>
(1)  First, 10% wrong solutions is too much for an AI.
     You may say "ok, in 20 years it will be perfect".
     Probably, it can be true, but I tell you about what I see now.

     By the way, my feeling is that good AI acceptable level for wrong solutions
     should be at most 1:1000, or 0.1%.



(2)  Second, it can be perfect in 20 years under one necessary condition: 
     the best minds in Math solving and writing and the best computer programming specialists 
     will work on it starting from now and during 20 years.


     What does it mean and why ? - Raising and educating a specialist in solving Math, writing Math 
     and explaining Math takes 10 - 15 - 20 years to get a professional level, when a person can speak, 
     write and teach professionally. (And, usually, the fingers of one hand are enough 
     to count such specialists of a national level in each country and in each generation).


     If you make such experiments with the novices, it will take 10-15-20 years for them to get a professional 
     level before they will learn to speak/write at the professional level, so it is a WRONG way to assign 
     novices for key positions for such an activity.


     It is the second conclusion from my arguments: the writers and the content creators must be professionals
     from the very beginning. Neither @mananth, nor @CPhill are such professionals.



(3)  Third, the computer codes which I see in the posts by @CPhill or @mananth, have no that level of flexibility
     to serve at the adequate level.  So, the level of the computer coders must be at least one order (one level) higher.



(4)  Fourth, the writing, coding and programming discipline must be changed.

     For now, the AI codes for solving school Math problems that I saw so far, do not show a tendency 
     to make checks of their solutions. They do not think that is is MANDATORY.  It is a crude error, which must be fixed.



(5)  Next.  As the life has taught me, many of incoming problems are mathematically non-sensical.
     So, the input flow is quite dirty, and therefore, idiotic incoming problems should be filtered out.
</pre>

OK. So, these are conclusions and directions from my overview that should be taken into account by developers of AI, 
if they want to have a perfect product in 20 years.



XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX



OK and very good.


There is one more issue, which I hesitate to pronounce.


It is well known fact that the peak in Math education in the world (in all industrially
developed countries) was from the middle of 1950s to, roughly say, 1970.
After that peak, the recession of the level of Math education was observed worldwide.


So and therefore, the specialists who are able to communicate with young students, 
to speak with them, to teach them Math, to inspire them and who got their Math education at that time,
have a special value.  People of this generation are quite old and will go out soon -
so and therefore, it is of great importance, great necessity and high urgency to use the experience 
of those of them, who still have a potential to share their knowledge, skills, style, tone, spirit and abilities.


When these people will go out totally, it will be too late.