Grades 7-8 Video Solutions 2025-2025_7-8

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Problem number 19. Sonya has two bowls of numbered balls. Bowl X contains seven balls numbered 1, 2, 6, 7, 10, 11, and 12. Bowl Y contains five balls numbered 3, 4, 5, 8, and 9.  Which balls should Sonya transfer from bowl X to bowl Y to increase the average number on the balls in each bowl?  To solve this problem, let's first figure out the average currently in each bowl. In the first bowl, we will add up all the numbers and divide by 7 since there are seven balls.  And the average in the first bowl, bowl X, is equal to 7. We do the same in the second bowl, bowl Y, and we get the average is equal to 5.8.  So now let's think about how we can increase the average in each bowl. First of all, we have to remove a ball from bowl X. And if we remove a ball from bowl X,  it should be lower than the average because we need to increase the average. And so if we take out something that's lower than the average, then the average of all the remaining  balls will go up. Similarly, we have to add a ball to bowl Y that is higher than the average because we need to increase the average in bowl Y. And so the ball that comes in must  be higher than the average to increase it. This means that the ball has to be higher than 5.8 but lower than 7 because those are the averages in bowls Y and X, respectively.  And the only whole number that's in the range from 5.8 to 7 is 6. And this is the only ball that's also in the list that we have that is between 5.8 and 7.  And so that means that the answer is A, 6.

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