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Every jump a game piece makes measures 8/9 . The piece starts at point A = 3 and jumps to the right. As soon as the piece jumps over B = 60, it switches direction and jumps to the left. The piece then stops at point C = −21. How many jumps did the game piece take?

Respuesta :

sqdancefan

Answer:

  157

Step-by-step explanation:

The number of jumps (p) in the positive direction will be the smallest integer value that satisfies ...

  3 + 8/9p ≥ 60

  8/9p ≥ 57 . . . . . . subtract 3

  p ≥ 57(9/8)

  p ≥ 64 1/8

The desired solution is p = 65. Then the final location in the positive direction is ...

  3 + 65(8/9) = 60 7/9

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From there to the final position of -21 is a distance of ...

  60 7/9 -(-21) = 81 7/9

The number of moves in the negative direction (n) is then ...

  n = (81 7/9)/(8/9) = (736/9)/(8/9) = 736/8 = 92

So, the total number of moves is the number the positive direction added to the number in the negative direction:

  moves = p + n = 65 + 92 = 157

The game piece took 157 jumps.

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