Grades 3-4 Video Solutions 2025-2025_3-4

Video Transcription

Question 24. A pair of scales is used to weigh three different objects, and the results are shown below.  Each type of object has a different mass. The masses can be 1, 2, 3, 4, or 5 kilograms.  What is the mass of one square in kilograms?  Let's start off by noticing that our stars, when there are two of them, weigh less than one square, and that when there are three squares, they weigh less than two circles.  This information, we know that the stars are the lightest, the circles are the heaviest, and the squares are somewhere in between.  We can start off by guessing how much the stars weigh.  Since two of them weigh less than one square, the stars will have to either weigh one or two kilograms.  However, if the stars weighed two kilograms each, the total weight would be four kilograms in the first scale, and the square would have to weigh five kilograms,  making it impossible for the circles to weigh more, so that cannot be the answer. So, the stars have to weigh one kilogram each.  This means that the square can weigh three, four, or five kilograms.  However, we've already established that the circles have to weigh more, so the square cannot weigh five kilograms.  Now, we have two options, and we can test this out on the second scale.  We have three squares here. Given the two different weight options, the total of the three squares would either be nine kilograms, three times three, or  twelve kilograms, three times four.  Now, this would also leave the circles with two options as well.  The circles could either weigh four or five kilograms.  However, if the circles weighed four kilograms, that would be a total of eight kilograms, and that number is smaller than either nine or twelve, so the circles cannot weigh this.  This information, we know the circles will have to weigh five kilograms each.  Knowing that, the squares cannot weigh four kilograms each, since that would weigh more than the circles do. So, the squares have to weigh three kilograms.  With this, we have figured out our solution, and it will be C, three.

Video Summary

The problem involves determining the mass of three objects of different weights, with each mass being 1, 2, 3, 4, or 5 kilograms. By analyzing the weighings, it is established that the stars are the lightest, the circles the heaviest, and the squares are intermediate. Stars weigh 1 kilogram each, as two stars weigh less than one square. Since circles are heavier, squares can't weigh 5 and must weigh 3 kilograms each. Circles weigh 5 kilograms each, given that three squares (9 kg) weigh less than two circles (10 kg). Thus, the mass of one square is 3 kilograms.