A grasshopper makes jumps that are either 17 or 19 cm in length, in either direction (forwards or backwards). Is it possible for the grasshopper to cover a distance of 101 cm in 100 jumps?

Question

Mathematics

Jameson Jones

6 January, 06:09

A grasshopper makes jumps that are either 17 or 19 cm in length, in either direction (forwards or backwards). Is it possible for the grasshopper to cover a distance of 101 cm in 100 jumps?

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Mathew Ayers · Answer 1

Answer: No. The grasshopper cannot cover exactly 101 cm in exactly 100 jumps.

Step-by-step explanation:

If the grasshopper makes 50 forward jumps of 19 cm and 50 backward jumps of 17 cm (in any order) the jumps total 950-850 for a net result of 100.

Changing to any other amount just gets farther away from the goal.

A system of equations yields no solution of integers.

x + y = =100

19x - 17y = 101

You can try it, but the result has a decimal. This grasshopper cannot make partial jumps!