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There are 28 more green balls than yellow balls. After 1/3 of the yellow balls and 3/7 of the green balls are removed, the number of yellow and green balls are the same. How many balls are there altogether at first?

 May 26, 2023
 #1
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G=28+Y -- what the equation translates too

4/7G=2/3Y -- the second sentence

12/21G=14/21Y -- multiplying each side so it is the same denominator

Notice the difference, 28 is 2/21, and 1/21 is 14.

Taking that into account: 14*21=294  294-28 is 266

294*4/7=168, 177+ 1/3. Hmmm.... wrong.. but notice that 168 and 177 +1/3 is relatively close. so the answer is around 294 for Green and 266 for blue. Hope this helps with checking your answer.

 May 26, 2023
 #2
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Y=Yellow,   G==Green


G ==Y + 28........................(1)


G - 3/7G ==4/7G - green balls remain
Y - 1/3Y ==2/3Y - yellow balls remain.


4/7G ==2/3Y......................(2), solve for G, Y


G ==196 - original number of green balls
Y ==168 - original number of yellow balls

 

Total =196 + 168 ==364 green and yellow balls at start

 May 26, 2023
edited by Guest  May 26, 2023

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