MO Z7-II-1 2020

Dragons and cyclops live on a fairy-tale island. All dragons are red, three-headed, and two-legged. All cyclops are brown, one-headed, and two-legged. Cyclops have one eye in the middle of their forehead; dragons have two eyes on each head. The cyclops and dragons together have 42 eyes and 34 legs in total. How many dragons and how many cyclops live on the island?

Final Answer:

d =  5
k =  12

Step-by-step explanation:

1k+2·3·d=42
2k+2·d=34

1·k+2·3·d=42
2·k+2·d=34

6d+k = 42
2d+2k = 34

Row 2 - 2/6 · Row 1 → Row 2
6d+k = 42
1.67k = 20


k = 20/1.66666667 = 12
d = 42-k/6 = 42-12/6 = 5

d = 5
k = 12

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