10. Paula the penguin goes fishing every day and always brings back twelve fish for her two chicks.
Each day, she gives the first chick she sees seven fish and gives the second chick five fish, which they eat. In the last few days one chick has eaten 44 fish. How many has the other chick eaten?
A 34
B 40
C 46
D 52
E 64
Solution
D

The first chick has eaten 44 fish in groups of seven and five. When you subtract multiples of five repeatedly from 44 , the only multiple of seven that is obtained is 14 . Therefore the first chick has eaten seven fish twice and five fish six times. Therefore, the number of times Paula went fishing is $2+6=8$ and so the number of fish she caught is $8 \times 12=96$. Therefore the number of fish the second chick has eaten in that time is $96-44=52$.