Answer to Question #329491 in Algebra for Shang

Question

Solve each of the following problems. Follow Polya's four stages of problem solving in your solution.

1. An egg vendor broke all the eggs that he was delivering to a local store. He could not remember how many eggs there were in all. However, he did remember that when he tried to pack them into packages of 2, 3, 4, 5, and 6 he had one left over each time. When he packed them into packages of 7, he had another left over. What is the smallest number of eggs he could have had in the shipment?

2. Edwin has 100 baseball cards. He wants to place the cards in three stacks so that the second stack has twice as many cards as the first, and the third stack has twice as many cards as the second. How many cards will be in each stack? How many will be left over?

Answer 1

1. LCM of 2,3,4,5,6,7 is 420 , so 421 will give a reminder by each of them. So the smallest number of eggs is 421

2. Let number of cards in first stack is X, then in second stack is 2X and in third stack 2(2)X=4X

X+2X+4X=100

X=100/7=14

2X=28

4X=56

Left over 100-56-28-14=2