3 Consider the set X = { 1 , 2 , 3 , 4 , 5 } and suppose you have two holes. Also suppose that you have 10 pigeons: the 2 -element subsets of X . Can you put these 10 pigeons into the two holes in a way that there is no 3 -element subset S = { a , b , c } ⊂ X for which all pigeons from S go in the same hole? Then answer the same question if X = { 1 , 2 , 3 , 4 , 5 , 6 } with 15 = C ( 6 , 2 ) pigeons.

Problem situation: caren is making rice and beans. she can spend no more than $10 on ingredients. she buys one bag of rice for $4.99. beans cost $0.74 per pound. how many pounds of beans, x, can she buy? inequality that represents this situation: 10≥4.99+0.74x drag each number to show if it is a solution to both the inequality and the problem situation, to the inequality only, or if it is not a solution.