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 foreheads, dragons have two eyes on each head. Cyclops and dragons have 42 eyes and 34 legs in total. How many dragons and how many cyclops live on the island?

Correct 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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