I have a bag, with some balls in it. All but four are blue, all but four are green, and all but four are red. In total, how many balls are there in the bag?

Question

asked Apr 19, 2023 61.5k views

1 Answer

JunaidKhan · Answer 1 · 2023-04-24T22:41:40+0000

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Step-by-step explanation:

x = total number of balls

x-4 = number of blue

x-4 = number of green

x-4 = number of red

3(x-4) = 3x-12 = total number of blue, green, or red

x - (3x-12) = x-3x+12 = -2x+12 = number of other colors

If there are other colors, then we want this quantity to be larger than 0, so,

-2x+12 > 0

-2x > -12

x < -12/(-2)

x < 6

There are less than 6 balls in the bag.

At the same time, we want each x-4 to be greater than zero

x-4 > 0

x > 4

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We found that x > 4 and x < 6

This combines to 4 < x < 6 which has us land on x = 5

This computes x-4 = 5-4 = 1, showing there's one of each blue, green and red. There are 5-1-1-1 = 2 balls of some other color not mentioned.

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If x = 6, then,

x-4 = 2 each of blue, green and red

There wouldn't be any other color since 6-2-2-2 = 0