Grades 1-2 Video Solutions 2025-2025_1-2

Video Transcription

Problem number 19. Charles has five wooden toys as shown in the picture. He picks two pairs of toys so that the pairs weigh the same. Which toy was not  picked? To solve this problem, first let's find the total weight of all the toys. That is 6 plus 8 plus 10 plus 11 plus 12 equals 47 grams. Now let's think about  the toy that we have to not pick. If we don't pick this toy, then the remaining toys can be divided into two pairs that weigh the same. But that means that the  remaining toys have to weigh an even amount, because an even number can be split into two parts that are equal. That is, if we take out one number, the total  of the remaining four numbers should be even, because it will be split into two equal parts. This means that we have to figure out which of the toys to  subtract out from 47 so that the result is even. But since 47 is an odd number, we have to subtract an odd number to result in an even number. That means that the  toy that we have to remove has to weigh an odd amount of grams. If we look at all the toys, the only one that's an odd number is 11, and it actually works. If we  ignore the 11 gram zebra, the remaining toys can be paired up like this. A 6 plus 12 gram toy weighs 18 grams in total, and an 8 plus a 10 gram toy weigh 18 grams  in total. Those two pairs are the same. Therefore, the answer is D.

Video Summary

Charles needs to exclude one toy so that the remaining toys can be divided into two pairs of equal weight. The total weight of all toys is 47 grams, which is odd. To achieve an even total when one toy is removed, it must be an odd-weight toy. The only toy weighing an odd amount is 11 grams. Removing the 11-gram toy results in a total of 36 grams, which can be split into two pairs: 6+12 and 8+10, both equaling 18 grams. Therefore, the toy not picked is the 11-gram one.

Keywords

toys

weight

pairs

odd

grams