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Answer:

86.5 green buttons

Explanation:

In a jar, there are pink, blue, green buttons.

They are divided in ratio forms:

  • pink : blue = 2 : 7

  • blue : green = 3 : 4

Make the ratio unit for the blue same, so that we can relate both together.

  • pink : blue = (2 : 7) * 3   ⇒ (6, 21)

  • blue : green = (3 : 4) * 7 ⇒ (21, 28)

All together :

  • pink : blue : green = 6 : 21 : 28

Let each button be "x"

  • 6x + 21x + 28x = 170

simplify

  • 55x < 170

divide both sides by 55

  • x < 3.091

So greatest green button:

  • 28 * 3.091
  • 86.54545
  • 86.5 green buttons    (rounded to nearest tenth)
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