Question

Blue balloons need 16 puffs to blow up, yellow balloons need 23, green balloons need 26 and red balloons need 32. Puffing Billy puffs all day long and puffs 1000 times altogether. Billy blows up twice as many blue balloons as yellow and half as many green balloons as red, but the same number of red balloons than yellow.

How many yellow balloons does Billy fill?

Answer 1

9514 1404 393

Answer:

  10 yellow balloons

Step-by-step explanation:

Let the numbers of blue, yellow, green, and red balloons be represented by b, y, g, r, respectively. The problem statement tells us the relations between these numbers are ...

  16b +23y +26g +32r = 1000

  b = 2y

  g = 1/2r

  r = y

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Using the second and third equations to substitute for b and g in the first, we have ...

  16(2y) +23y +26(1/2r) +32r = 1000 . . . . substitute for b and g

  55y +45r = 1000 . . . . . simplify

Using the last equation to substitute for r gives ...

  100y = 1000

  y = 1000/100 = 10

Billy fills 10 yellow balloons.

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Additional comment

He also fills 10 red balloons, 20 blue balloons, and 5 green balloons.