Grades 7-8 Video Solutions 2024-2024_7-8

Video Transcription

Problem number 26. Farmer Frank is selling chicken and duck eggs. He has baskets holding 4, 6, 12, 13, 22, and 29 eggs. His first customer buys all the eggs  in one basket. Frank notices that the number of chicken eggs he has left is twice the number of duck eggs. How many eggs did the customer buy? So first,  let's assign variables to the situation. After the customer buys one basket, let's say x is the number of duck eggs. Then there are 2x chicken eggs. So in total,  there are x plus 2x equals 3x eggs. This means that the number of eggs has to be a multiple of 3 after the customer buys a basket. Well, we know that initially  Frank had a total of 4 plus 6 plus 12 plus 13 plus 22 plus 29 equals 86 eggs. And we know that afterwards Frank had a number of eggs that was a multiple of  3. Since 86 leaves a remainder of 2 when divided by 3, the number of eggs sold also has a remainder of 2 when divided by 3. Because that means after we  subtract out this value, the result will have a remainder of 0 when divided by 3. And if something has a remainder of 0 when divided by 3, that means it is a  multiple of 3, which we know is true. So we just have to check the remainders for all the baskets and see which of them has a remainder of 2 when  divided by 3. And if we look at them, we get 4 has a remainder of 1, 12 has a remainder of 0, 13 has a remainder of 1, 22 has a remainder of 1, and 29 has a  remainder of 2. And remember, we need to find which of these has a remainder of 2 because after we subtract from 86, which also has a remainder of 2, we should end  up with a remainder of 0. The only one of these that has a remainder of 2 when divided by 3 is 29. So the answer is E, 29.

Video Summary

Farmer Frank has baskets of eggs with 4, 6, 12, 13, 22, and 29 eggs. After his first customer buys one basket, he is left with twice as many chicken eggs as duck eggs, meaning the remaining eggs are a multiple of 3. Initially, Frank had 86 eggs, which leaves a remainder of 2 when divided by 3. To find which basket the customer bought, we look for a basket that also leaves a remainder of 2 when divided by 3, allowing the remainder for the remaining eggs to be 0. The basket with 29 eggs satisfies this condition. Thus, the customer bought 29 eggs.