Problem number 13. Every time the kangaroo goes up seven steps, the rabbit goes down three steps. On which step do they meet? A, 53. B, 60. C, 63. D, 70. E, 73. In addition to what we know from the problem, we can see that there are 100 steps on the stairs. The kangaroo and the rabbit are moving at the same time. The kangaroo moves up seven steps while the rabbit goes down three steps. So we can think of this as moves of seven plus three or ten steps each. To cover all 100 steps, they need to make 100 divided by 10 or 10 moves. This means that after 10 moves they will meet. Now we just need to figure out which step that is. In 10 moves, the kangaroo goes up 10 times 7, which is 70 steps. So he will land on step number 70. Also the rabbit will move 3 times 10 or 30 steps. If he starts at step 100 and goes down 30 steps, he also will end up at step 70, which confirms our answer. So they will meet on step 70. The answer is D, 70.

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