Grades 3-4 Video Solutions 2021-video 2021 3-4/22

Video Transcription

Problem number 22. Each of the 5 boxes contains either apples or bananas, but not both. The total weight of all the bananas is 3 times the weight of all the apples.  Which boxes contain apples? A. Boxes 1 and 2 B. Boxes 2 and 3 C. Boxes 2 and 4 D. Boxes 3 and 4 or E. Boxes 1 and 2  In this type of problem, it's good to first stop and think through what it means that the total weight of the bananas is 3 times the weight of the apples.  It means that for each unit of weight of apples, we have 3 units of weight of bananas.  Or, that 1 fourth of the weight is apples  and 3 fourths of the weight is bananas.  Now, we can figure out the total weight of all the fruit given the boxes, figure out what 1 fourth of that weight is,  and from there, try to find the boxes that would contain that weight exactly. Adding up the weights here, we have 5 plus 2 kilograms, that's 7 kilograms, plus 7 more gives us 14,  add the 14 to 16 to get 30 kilograms, and then plus the 6 gives us 36 kilograms total.  We already figured out that the apples are 1 fourth of the total weight.  So, we can do 36 times 1 fourth, or very simply, 36 divided by 4  to find the weight of the apples. 36 divided by 4 is 9. So, the apples weigh 9 kilograms.  Now, let's look at the weights marked on the boxes. We have 7 kilograms, 5 kilograms, 6 kilograms, 2 kilograms, and 16 kilograms.  Obviously, it will not be the 16 kilograms because that's too much weight already. Looking at the other boxes, we see that we can make 9 kilograms  by using the box that has the 2 kilograms and the one that has 7 kilograms, or boxes 1 and 4.  Boxes 1 and 4 is answer choice E. So, that is the answer.

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