Grades 7-8 Video Solutions 2024-2024_7-8

Video Transcription

Problem number 14. Paula the penguin goes fishing every day and always brings back 12 fish for her  two chicks. Each day she gives the first chick she sees 7 fish and gives the second chick 5 fish  which they eat. In the last few days one chick has eaten 44 fish. How many has the other chick eaten?  So the first thing to note is this value 44 is equal to the sum of some number of fives and  some number of sevens because each day we either get 5 fish or 7 fish to a chick and so that means  that this is equal to a multiple of 5 plus a multiple of 7. If we list out all of the multiples  of 5 we can try and see could we add a multiple of 7 to make this equal to 44 or in other words  if we do 44 minus a multiple of 5 can we get a multiple of 7. If we list out 44 minus the  multiples of 5 we see that the first one that is a multiple of 7 is 14 and so that means that 44  is equal to 5 times 6 which is 30 plus 7 times 2 which is 14 and that means that this first chick  has eaten 5 fish on six of the days and 7 fish on the other two days. And the question asked is how  much has the other chick eaten? Well the other chick has to eat 7 fish on those six days and 5  fish on the other two days because we know that the other chick eats whatever the first chick  didn't and so that chick eats a total of 7 times 6 plus 5 times 2 fish which is equal to 42 plus 10 or 52 so the answer is D 52.

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