Tutors Answer Your Questions about Reduction-of-unit-multipliers (FREE)
Question 1207935: How to convert 42.27 lb-s^1/ft^-1 to hp? I know that 550 lb-ft/s is equal to 1 hp but I do not know how to continue solving it since there are negative exponents in the given problem and the ft and s are switched. Thank you so much!
Answer by ikleyn(52803)   (Show Source):
You can put this solution on YOUR website! .
How to convert 42.27 lb-s^1/ft^-1 to hp? I know that 550 lb-ft/s is equal to 1 hp
but I do not know how to continue solving it since there are negative exponents
in the given problem and the ft and s are switched. Thank you so much!
~~~~~~~~~~~~~~~~~~~
"hp" in this post is the "horse power", a unit of mechanical power.
First, the dimension lb-s^1/ft^-1 (at 42.27 in your post)
is the same as the dimension lb-ft/s (at 550 in your post).
+----------------------------------------------------------------+
| So, there is NO any trouble with the dimension units: |
| they are consistent, they are simply the same dimension unit. |
+----------------------------------------------------------------+
Second, if 550 lb-ft/s is 1 hp, then 42.27 lb-ft/s is  = 0.0769 hp.
That's all.
Solved, answered and explained.
Don't intimidate or confuse yourself.
Question 1206963: 2tan(x)sin(x)+2sin(x)=tan(x)+1. x is has to be from 0 to 360 inclusive.
Solve for all values of x
Answer by ikleyn(52803) (Show Source):
Question 559646: a car radiator has a capacity of 16 quartz and is filled with a 25% antifreeze solution. how much must be drained off and replaced with pure antifreeze to obtain a 40% antifreeze solution?
Found 3 solutions by greenestamps, josgarithmetic, mananth:
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
The "draining off" and "replacing" in the problem only complicates the process of solving the problem. Essentially, you are simply mixing a 25% antifreeze solution with a 100% antifreeze solution to obtain 16 quarts of 40% antifreeze.
The question asks for the amount of pure antifreeze to be used. So
x = quarts of 100% antifreeze
16-x = quarts of 25% antifreeze
The mixture is 40% antifreeze:
I leave it to you to solve the problem by that formal algebraic method. As shown the the other tutors, the answer is 3.2 quarts.
Here is an informal method that can be used to solve any 2-part mixture problem like this.
The three percentages in the problem are 25, 40, and 100. Picture (in your mind, or on paper if needed) those three percentages on a number line. Then observe/calculate that 40 is 15/75 = 1/5 of the way from 25 to 100. That means 1/5 of the mixture is the 100% antifreeze.
1/5 of 16 quarts is 3.2 quarts.
ANSWER: 3.2 quarts
Answer by josgarithmetic(39620) (Show Source):
Answer by mananth(16946)  (Show Source):
You can put this solution on YOUR website! a car radiator has a capacity of 16 quartz and is filled with a 25% antifreeze solution. how much must be drained off and replaced with pure antifreeze to obtain a 40% antifreeze solution?
Initial conc = 25%Final conc = 40%
100% antifreeze x qts
Antifreeze to be removed =x
(16-x)*0.25+1*x = 0.4(16)
4-0.25x +x = 6.4
0.75x = 2.4
x = 3.2 qts
Question 657575: A pack of elephants are moving at 6 mph. One gets left behind. It chased at a rate of 10 mph and caught up in 5 minutes. Howlong in hours did it run to catch up? How far did the lone elephant run?
Found 2 solutions by greenestamps, mananth:
Answer by greenestamps(13200) (Show Source):
You can put this solution on YOUR website!
The solution from tutor @mananth assumes the pack of elephants stops to wait for the lone elephant to catch up, so that the lone elephant catches up to the pack at a rate of 10mph.
More likely, the pack kept moving at 6mph, so the rate at which the lone elephant catches up is 10-6 = 4mph.
ANSWERS:
The lone elephant ran for 5 minutes to catch up; 5 minutes is 1/12 of an hour.
The lone elephant ran for 1/12 of an hour at 10mph to catch up; the distance it ran to catch up was 10*(1/12) = 5/6 miles.
Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website! A pack of elephants are moving at 6 mph. One gets left behind. It chased at a rate of 10 mph and caught up in 5 minutes. Howlong in hours did it run to catch up? How far did the lone elephant run?
Let the catchup distance be x miles
time to catchup 5 minutes= 5/60 hours = 1/12 hours
rate of lone elephant = 10mph
D= s*t
D= 1/12 * 10 =5/6 m
Question 793048: Kat spends 30 minutes of time partly in listening to her professor and partly in text messaging her close friends. The time she spends on text messaging is 2 times more than what she spends listening to her professor. How many minutes does Kat spend listening to her professor?
Found 2 solutions by greenestamps, mananth:
Answer by greenestamps(13200) (Show Source):
You can put this solution on YOUR website!
The answer shown by the other tutor is very probably the intended answer to the problem. However, it is the wrong answer, because very probably the problem was written incorrectly.
Any math problem written using any form of a phrase like "2 times more than" is an invalid problem, because nearly everybody interprets that phrase incorrectly.
If I spend 2 TIMES AS MUCH time on one task as I do on another, then the amount of time I spend on one task can be represented by x, and the time I spend on the other task can then be represented as 2x.
But if I spend 2 TIMES MORE on one task as I do on another, and the amount of time I spend on the shorter task is x, then the amount of time I spend on the longer task is the amount of time I spend on the shorter task, PLUS 2 TIMES MORE that amount of time -- i.e., x + 2x = 3x.
In everyday sloppy language, "2 times as much as" and "2 times more than" are used to mean the same thing, but they do not.
With the grammatically correct interpretation of the question as written....
x = amount of time spent listening to her professor
3x = amount of time spent text messaging
The total time is 30 minutes:
(correct) ANSWER: Kat spends 7.5 minutes listening to her professor
Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website! Kat spends 30 minutes of time partly in listening to her professor and partly in text messaging her close friends. The time she spends on text messaging is 2 times more than what she spends listening to her professor. How many minutes does Kat spend listening to her professor?
Let her listen to the professor for x minutes
The time she spends on text messaging is 2 times more than what she spends listening to her professor. How many minutes does Kat spend listening to her professor?
2x = 2x hours
2x+x = 1/2 hour
3x = 1/2
x= 1/6 hours =10 minutes
Question 1027688: The area of triangle ABC is trisected by two segments parallel to base BC. The longer of these segments is 24 cm. What is the length of base BC? Express your answer in simplest radical form.
Found 3 solutions by greenestamps, ikleyn, mananth:
Answer by greenestamps(13200) (Show Source):
Answer by ikleyn(52803) (Show Source):
Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website! The area of triangle ABC is trisected by two segments parallel to base BC. The longer of these segments is 24 cm. What is the length of base BC? Express your answer in simplest radical form.
Triangle ABC znd triangle AFG are similar
Triangle ABC /triangle AFG = BC^2/FG^2
3/2 = BC^2/FG^2
3/2 = BC^2/12^2
BC^2= 3/2 * 12^2
BC = sqrt( 3/2*12^2)
BC = 12sqrt(6)
Question 687224: The ratio of the numerator to the denominator of a certain fraction is five to eight. If five is subtracted from the numerator and four is added to the denominator, the new fraction reduces to one-half. What is the original fraction?
A mixture contains
A girl is now
Found 3 solutions by greenestamps, ikleyn, mananth:
Answer by greenestamps(13200) (Show Source):
Answer by ikleyn(52803) (Show Source):
You can put this solution on YOUR website! .
One and ONLY ONE problem/question per post.
It is the RULE, the POLICY and the REQUIREMENT of this forum.
It is written in this page
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from which you post your problems.
It is assumed that you read these rules before posting.
It is also assumed that you do understand what is written in that page and follow the rules.
Those who violate them, work against their own interests.
Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website! The ratio of the numerator to the denominator of a certain fraction is five to eight. If five is subtracted from the numerator and four is added to the denominator, the new fraction reduces to one-half. What is the original fraction?
let numerator be x and denominator be y
x/y = 5/8
y= 8x/5
If five is subtracted from the numerator and four is added to the denominator, the new fraction reduces to one-half.
(x-5)/(y+4) =1/2
2(x-5)=(y+4)
2x-10= y+4
2x-y = 14
2x- (8x/5)=14
multiply by 10
20x -16x = 140
4x=140
x=35
y=56
the original fraction is 35/56
Question 801507: The wheels on a certain bicycle have a radius of 13.2 inches. Suppose the wheels roll at 150 revolutions per minute along flat ground without slipping. How fast is the bicycle moving in miles per hour?
The question then hints to convert revolutions to radians per minute, but I am unsure how to do this and any help on what to do to get the answer would be greatly appreciated! Thank you!
Found 3 solutions by ikleyn, josgarithmetic, mananth:
Answer by ikleyn(52803) (Show Source):
You can put this solution on YOUR website! .
The wheels on a certain bicycle have a radius of 13.2 inches. Suppose the wheels roll
at 150 revolutions per minute along flat ground without slipping.
How fast is the bicycle moving in miles per hour?
The question then hints to convert revolutions to radians per minute, but I am unsure
how to do this and any help on what to do to get the answer would be greatly appreciated! Thank you!
~~~~~~~~~~~~~~~~
The answer in the post by @mananth is incorrect.
I came to bring a correct solution/answer.
bicycle radius of 13.2 inches.
One revolution covers a distance 2pir = 2*pi*13.2 inches.
150 revolutions per minute cover
150*2*pi*13.2 inches/minute = 12440.707 inches/minute.
1 mile =63360 inches
1 hour = 60 minutes
So, 150 revolutions per minute is the same speed as
 = 11.781 miles per hour.
ANSWER. 11.781 miles per hour.
Solved, giving a correct answer.
Answer by josgarithmetic(39620) (Show Source):
Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website! The wheels on a certain bicycle have a radius of 13.2 inches. Suppose the wheels roll at 150 revolutions per minute along flat ground without slipping. How fast is the bicycle moving in miles per hour?
The question then hints to convert revolutions to radians per minute, but I am unsure how to do this and any help on what to do to get the answer would be greatly appreciated! Thank you!
bicycle radius of 13.2 inches
One revolution covers a distance 2pir = 2*pi*13.2 inches
150 revolutions pwr minute 150*2*pi*13.2 inches=
12 440.707inches/minute
1 mile =63360 inches
1 hour = 60 minutes
12 440.707/63360*60)
0.00327 miles/hour
Question 789015: An open rectangular box is to be made from a piece of cardboard 20 inches wide and 20 inches long by cutting a square from each corner and bending up the sides.
(a) Express the volume V of the box as a function of the size x of the cutout.
Found 2 solutions by ikleyn, mananth:
Answer by ikleyn(52803) (Show Source):
Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website! An open rectangular box is to be made from a piece of cardboard 20 inches wide and 20 inches long by cutting a square from each corner and bending up the sides.
(a) Express the volume V of the box as a function of the size x of the cutout.
2
Volume of box = x*(20-2x)(20-2x) cu.in
x((400 -80x+4x^2)=V
4x^3-80x^2+400x = V
(rectified)
Question 559649: monica drove to work on monday at 40 miles per hour and arrived one minute late. she left the same time on tuesday, drove at 45 miles per hour, and arrived one minute early. how far does monica drive to work?
Found 2 solutions by ikleyn, mananth:
Answer by ikleyn(52803) (Show Source):
You can put this solution on YOUR website! .
monica drove to work on monday at 40 miles per hour and arrived one minute late.
she left the same time on tuesday, drove at 45 miles per hour, and arrived one minute early.
how far does monica drive to work?
~~~~~~~~~~~~~~~~~~~~~~
Let d be the distance Monica drives to work, in miles.
Driving at the speed of 40 mph, he spends  hours.
Driving at the speed of 45 mph, he spends  hours.
The difference of these time intervals is 2 minutes, or  of an hour.
So, we write this equation
- = .
Multiply both sides by 360. You will get
9d - 8d = 12,
d = 12.
ANSWER. The distance is 12 miles.
Solved.
------------------
It is a standard classic elegant solution to this problem.
This problem is designed, created and exists to be solved
by the method shown in my post.
The problem is created to teach students solving similar problems
by using "time equation". Learning this method, students will be
fascinated by its beauty. That's the point of this task.
Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website! monica drove to work on monday at 40 miles per hour and arrived one minute late. she left the same time on tuesday, drove at 45 miles per hour, and arrived one minute early. how far does monica drive to work?
Let time to be be taken to reach on time be t
Let distance be x miles
monica drove to work on monday at 40 miles per hour and arrived one minute late.
x/40 = t+1/60
multiply by 120
3x=120t+2
3x-120t=2.................1
monica drove to work on Tuesday at 45 miles per hour and arrived one minute early.
x/45 = t-1/60
multiply by 180
4x = 180t-3
4x-180t=-3..................2
solve for x &t
Multiply (1)by 4 and (2)3
12x-480t=8
12x-540t=-9
60 t=17
t= 17/60
plug t
x= 12 miles
Question 794453: a car and bus leave from the same spot and drive in opposite directions. the bus is travelling 6 miles per hour slower than the car. in 4.50 hours, the car and the bus are 217 miles apart. find the average speed of the car
Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website! a car and bus leave from the same spot and drive in opposite directions. the bus is travelling 6 miles per hour slower than the car. in 4.50 hours, the car and the bus are 217 miles apart. find the average speed of the car
Let speed of car be x m/hr
Bus speed will be (x-6) m/hr
they are moving in opposite directions
d= s*t
4.5x+4.5(x-6)=217
9x-27=217
9x= 244
x=27.11
The average speed of the car is approximately 27.11 miles per hour
Question 1130221: Use a model to determine the amount owed on a loan of $5,000 with simple interest of 4.25%. The model was A=5000+5000(0.0425t), where A is the amount (total principal plus interest) required to repay a loan, and t is the time, in years.
What is the slope of this model? Include units in your answer.
How long would it take for the loan amount to reach $7,000? Round to the nearest tenth.
Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website! Use a model to determine the amount owed on a loan of $5,000 with simple interest of 4.25%. The model was A=5000+5000(0.0425t), where A is the amount (total principal plus interest) required to repay a loan, and t is the time, in years.
What is the slope of this model? Include units in your answer.
How long would it take for the loan amount to reach $7,000? Round to the nearest tenth.
A=5000+5000(0.0425t)
A= 212.5t +5000
compare with y=mx+c
Slope = m= 212.5
A=7000
A= 212.5t +5000
7000 = 212.50t+5000
2000/212.50=t
t= 9.412 years
Question 1205692: two more than seven times Lynn’s age
Found 2 solutions by greenestamps, josgarithmetic:
Answer by greenestamps(13200) (Show Source):
You can put this solution on YOUR website!
For a beginning algebra student, it can be hard to learn to interpret the given words correctly....
"two more than seven times Lynn’s age"
Note the "two more than ..." means you are starting with the "..." and adding 2. So the algebraic expression is going to be of the form (...) + 2.
"seven times ..." means you are multiplying "..." by 7. "seven times Lynn's age" means you are multiplying Lynn's age by 7.
So let x be Lynn's age
Then "seven times Lynn's age" is 7x
And then "two more than seven times Lynn’s age" is 7x + 2.
Note that many beginning students, by looking at the words exactly as they are given without thinking of their meaning, will write the given expression as 2 + 7x. The expressions "7x + 2" and "2 + 7x" are algebraically equivalent; however, "7x + 2" is a better representation, because -- again -- "two more than seven times Lynn’s age" means you are starting with 7 times Lynn's age and adding 2.
If the same student, by reading the words directly without thinking about what they mean, interpreted "2 less than Lynn's age" as "2 - 7x", that would clearly be wrong, because the written expression means you are starting with 7 times Lynn's age and subtracting 2. So the correct algebraic expression would be "7x - 2" instead of "2 - 7x".
The student needs to learn to look at the meaning of the given expression in words to write the correct algebraic expression.
Answer by josgarithmetic(39620) (Show Source):
Question 1205404: The telephone poles along a road are 20m apart and a car travels from the first to the fifteenth in 10½ seconds. Calculate the speed of the car in km/h.
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52803) (Show Source):
Answer by math_tutor2020(3817) (Show Source):
Question 1204570: Use six unit multipliers to convert 28,000 square inches to square meters.
Found 2 solutions by math_tutor2020, josgarithmetic:
Answer by math_tutor2020(3817) (Show Source):
Answer by josgarithmetic(39620) (Show Source):
You can put this solution on YOUR website! Already answered
Wait. Six unit multipliers? Square units to square units? You only will need four unit multipliers. The two of them done twice each.
Question 1204572: Use six unit multipliers to convert 28,000 square inches to square meters.
Answer by josgarithmetic(39620) (Show Source):
Question 1203335: A bicycle is traveling at 22 miles per hour. How many feet will it cover in 35 seconds? Round your answer to the nearest tenth of a foot
Found 5 solutions by Alan3354, Edwin McCravy, math_tutor2020, josgarithmetic, ikleyn:
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! A bicycle is traveling at 22 miles per hour. How many feet will it cover in 35 seconds? Round your answer to the nearest tenth of a foot
----------
From memory, 15 mi/hr = 22 ft/sec
--> 1 mi/hr = 22/15 ft/sec
22 mi/hr = 484/15 ft/set
d = 35*484/15 feet
-------------
No need for a Master's Thesis
Answer by Edwin McCravy(20060)  (Show Source):
Answer by math_tutor2020(3817) (Show Source):
You can put this solution on YOUR website!
Answer: 1129.3 feet (approximate)
=================================================================================
Explanation
I'll go over two methods.
Method 1
We're given a speed in miles per hour (mph), and we want to determine the number of feet traveled in 35 seconds.
Let's convert from miles per hour to feet per second.
I'll use the railroad track conversion method.
We have 22 miles over 1 hour in the first column
Each subsequent column is one of the equivalences below
5280 ft = 1 mile
1 hour = 60 min
1 min = 60 sec
Take note how I placed each unit so we have "miles", "hours", and "minutes" cancel out.
The goal is to be left with "feet" up top and "seconds" down below.
Multiply straight across the numerators to get: 22*5280*1*1 = 116,160
Do the same for the denominators: 1*1*60*60 = 3600
Divide the results: 116160/3600 = 32.2666666666667 approximately
Therefore, 22 mph = 32.2666666666667 feet per second approximately
Similar conversion questions
https://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.1202485.html
and
https://www.algebra.com/algebra/homework/Percentage-and-ratio-word-problems/Percentage-and-ratio-word-problems.faq.question.1200497.html
Then,
distance = rate*time
distance = (32.2666666666667 feet per sec)*(35 sec)
distance = 1129.33333333333 feet approximately
distance = 1129.3 feet approximately when rounding to the nearest tenth of a foot.
------------------------------------------------------------
Method 2
1 hour = 60 min
1 min = 60 seconds
1 hour = 60*60 = 3600 seconds
1 second = 1/3600 of an hour
35 seconds = 35/3600 of an hour = 7/720 of an hour
distance = rate*time
distance = (22 mph)*(7/720 of an hour)
distance = 0.21388888888889 miles approximately
Then we convert from miles to feet.
1 mile = 5280 feet
0.21388888888889*1 mile = 0.21388888888889*5280 feet
0.21388888888889 mile = 1129.33333333333 feet approximately
0.21388888888889 mile = 1129.3 feet approximately
Whichever method you use, be very careful about your units.
Answer by josgarithmetic(39620) (Show Source):
Answer by ikleyn(52803) (Show Source):
You can put this solution on YOUR website! .
A bicycle is traveling at 22 miles per hour. How many feet will it cover in 35 seconds?
Round your answer to the nearest tenth of a foot
~~~~~~~~~~~~~~~~~~~~~
1 mile = 5280 feet.
To answer your question, first multiply 5280 feet by 22 and divide by 3600, the number of seconds in an hour.
You will get the number of feet covered in 1 second.
To get the answer, multiply it by 35 seconds. You may combine everything in one line formula
ANSWER =  .
Use your calculator and round as requested.
Happy calculations (!)
/////////////////
Since after my post, @josgaritmetic came with his answer of 1064.8 feet,
I must refute it as incorrect.
The correct answer is 1129.3 feet.
\\\\\\\\\\\\\\\\\\
Looking at the super-bulky solutions by other tutors to this super-simple problem,
I want to explain to the visitor that the educational meaning of this problem
is to develop common sense - not to develop this bulky technique.
To learn the subject on conversion units, look into the lessons
- Units conversion examples
- Converting feet to meters, inches to centimeters, miles to kilometers and vice versa
- Converting speed units: miles per hour to kilometers per hour and vice versa
- Converting measures of volume: cubic feet and cubic meters
- Converting liquid volume measures: liters, gallons, and barrels
in this site.
Learn from there all you need to know - once and forever.
Consider these lessons as your textbook, handbook, guidebook, tutorials
and free of charge home teacher, who is always and everywhere with you - to help and to teach.
Question 1202348: The prairie dogs were having a town meeting to talk about the blackfooted ferret that was terrorizing the neighborhood. One town council dog suggested building a network of tunnels connecting every burrow to every other burrow. Then someone said Are you crazy ? We have nine burrows. Thats too many tunnels nd too much money to build them. If each tunnel cost $1.00 to build, how much would it cost the prairie dogs to connect every burrow with every other burrow?
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3817) (Show Source):
You can put this solution on YOUR website!
Answer: 36 tunnels
Total cost = $36
====================================================================
Explanation:
Let's say for example there are 5 burrows labeled A,B,C,D,E.
Make a 5 by 5 table with those labels along the left and top side.
It's clear it makes no sense to build a tunnel connecting any given burrow to itself. We cannot connect A to A for instance.
Let's cross those entries out with an X.
The 5*5 = 25 entries has now dropped to 25-5 = 20 entries. We've subtracted off the 5 cells marked with X.
In other words:
25 - 5
5*5 - 5*1
5*(5-1)
5*4
Meaning that if we had n burrows, then we'd have n^2 - n = n*(n-1) entries after removing the northwest diagonal.
But notice the symmetry of the table. The entries marked with Y represent connecting burrow A to C
We've double-counted things when marking two instances of Y.
So we ignore either the lower half or the upper half. The string of X's is the divider line.
This means we'll divide by 2 when ignoring half of the cells of the table.
There are 5*4/2 = 20/2 = 10 different tunnels connecting the five burrows together.
The ten tunnels are:
AB
AC
AD
AE
BC
BD
BE
CD
CE
DE
A tunnel like AB is the same as BA. Order doesn't matter.
The formula in general is n*(n-1)/2 which is found in the nCr formula when r = 2.
If we had n = 9 burrows, then,
n*(n-1)/2
9*(9-1)/2
9*8/2
72/2
36
There are 36 tunnels connecting the 9 burrows to each other. Each tunnel costs $1.00, which means the total cost is $36.
Answer by ikleyn(52803) (Show Source):
Question 1202350: The prairie dogs were having a town meeting to talk about the blackfooted ferret that was terrorizing the neighborhood. One town council dog suggested building a network of tunnels connecting every burrow to every other burrow. Then someone said Are you crazy ? We have nine burrows. Thats too many tunnels nd too much money to build them. If each tunnel cost $1.00 to build, how much would it cost the prairie dogs to connect every burrow with every other burrow
Answer by ikleyn(52803) (Show Source):
Question 1202349: Lloyd gave 1/2 his marbles to Lee. Then, he gave 2/3 of the remaining ones to Lynn. If he ended up with ten marbles, how many did he have when started?
Found 2 solutions by josgarithmetic, mananth:
Answer by josgarithmetic(39620) (Show Source):
Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website! Lloyd gave 1/2 his marbles to Lee. Then, he gave 2/3 of the remaining ones to Lynn. If he ended up with ten marbles, how many did he have when started?
Let him have x marbles initially
gave 1/2 his marbles to Lee
x/2
remaining with him
x-x/2= x/2
2/3 of the remaining ones to Lynn
2/3(x/2)= x/3
x-x/2-x/3 = 10
simplify
Multiply by LCM 6
6x-3x-2x=60
x=60 Llyod had 60 marbles initially
Question 1202222: Rainbow Robots Inc. was putting on a big demomstration. Everyone came to watch the colorful robotswash the windows at the Miller building. First the big red robot washed one half of all the windows in the building. Then the smaller green robot washed one half of the windows that were left. To the cheers of everyone watching, the tiny yellow robot washed the last 10 windows. How many windows did the rainbow robots wash altogether?
Found 4 solutions by math_tutor2020, greenestamps, MathTherapy, mananth:
Answer by math_tutor2020(3817) (Show Source):
You can put this solution on YOUR website!
Answer: 40
Explanation:
We can draw a rectangle to represent all of the windows.
Split the rectangle in half to allocate those windows to the red robot.
The other half is then split in half to get two quarters.
One of those quarters is allocated to the green robot.
The yellow robot gets the other quarter.
Here's what the diagram could look like
x = number of windows total
1/4 of x = number of windows the yellow robot washed
x/4 = 10
x = 4*10
x = 40 windows total
Answer by greenestamps(13200) (Show Source):
You can put this solution on YOUR website!
The problem can easily be worked informally by working backwards, using logical reasoning.
The green robot washed half of the windows that were left when it started working. That means it left half of the windows unwashed. Those are the 10 windows that the last robot washed. So when the green robot started washing windows, the number left to be washed was 2(10) = 20.
Similarly, the red robot washed half of all the windows, so the 20 windows it left unwashed were half of the total number of windows, making the total number of windows 2(20) = 40.
ANSWER: 40
Answer by MathTherapy(10552)  (Show Source):
Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website! Rainbow Robots Inc. was putting on a big demomstration. Everyone came to watch the colorful robotswash the windows at the Miller building. First the big red robot washed one half of all the windows in the building. Then the smaller green robot washed one half of the windows that were left. To the cheers of everyone watching, the tiny yellow robot washed the last 10 windows. How many windows did the rainbow robots wash altogether?
You may edit the question. Maybe convert formulae to the same
let totalnumber of windows be x
the big red robot washed one half of all the windows in the building.
x/2
Remaining windows x/2
he smaller green robot washed one half of the windows that were left.
1/2 *(x/2)=x/4
tiny yellow robot washed the last 10 windows.
10
x/2 +x/4 +10 =x
LCM =4
multiply all terms by 4
(x/2)*4 +(x/4)*4 +(10)*4 =4x
2x +x +40 =4x
3x+40 =4x
subtract 3x on both sides of equation
3x-3x +40 = 4x -3x
x=40
The rainbow robots washed altogether 40 windows
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