Grades 9-10 Video Solutions 2022-2022_9-10

Video Transcription

Question 15. Three children asked their grandmother how old she was. She replied by asking them  to guess her age. One child said she was 75. One said she was 78. And one said she was 81. It turned out that one of the guesses was wrong by one year. One was wrong by two  years. And one was wrong by four years. What is the grandmother's age? You can start off by setting two of these sets next to each other. Now, one of them was wrong by four  years. So we can put this most extreme value on either the beginning or the end. So in the first set, let's add four to the lowest value. And in the second set, let's subtract  four from the highest value. And this gives us 79 and 77. Now all we have to do is make the other values match. So we can add the one to 78 and get 79. And then we can add  the one that was wrong off by two years, subtract it from 81 and get 79. In the second set where  we got 77 and subtract one and get 77. And we can add two to 75 and get 77. With this,  we noticed that there were two different possible solutions. The grandmother could be 79 or she could be 77. So the answer will be E. It cannot be determined exactly.

Video Summary

The problem involves deducing a grandmother's age based on incorrect guesses by her grandchildren. Guesses were 75, 78, and 81, each wrong by 1, 2, or 4 years. By adjusting for the error, two possible ages are found: 79 and 77. Therefore, the exact age cannot be determined from the provided information, making the solution indeterminate.