SOLUTION: 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 o

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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 mananth, MathTherapy, greenestamps, math_tutor2020:
Answer by mananth(16946) About Me  (Show Source):
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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



Answer by MathTherapy(10552) About Me  (Show Source):
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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?

Let number of windows be W
Number of windows washed by red robot: matrix%281%2C3%2C+%281%2F2%29W%2C+or%2C+W%2F2%29
Number of unwashed windows after red robot washed: matrix%281%2C3%2C+%281%2F2%29W%2C+or%2C+W%2F2%29
Number of windows remaining after green robot washed 1%2F2 of remainder: 
Number of unwashed windows left for yellow robot to wash: 10 (given)
Fraction representing the number of unwashed windows left for yellow robot to wash: W%2F4
        We then get: matrix%281%2C3%2C+10%2C+%22=%22%2C+W%2F4%29
Number of windows or highlight_green%28matrix%281%2C5%2C+W%2C+%22=%22%2C+10%284%29%2C+%22=%22%2C+40%29%29 ------ Cross-multiplying

You could also do this BACKWARDS:
Final number of unwashed windows for yellow to wash: 10
Before GREEN washed 1%2F2 of remaining windows AFTER RED washed, number of unwashed windows: matrix%281%2C5%2C+10%2F%281%2F2%29%2C+%22=%22%2C+10%282%29%2C+%22=%22%2C+20%29
Before RED washed 1%2F2 of TOTAL number of windows, number of unwashed windows:

Answer by greenestamps(13200) About Me  (Show Source):
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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 math_tutor2020(3817) About Me  (Show Source):
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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