Can someone explain to me why this is right?

Graph red beads cost $1 an ounce and gold beads cost $3 an ounce. juanita wants to purchase a 12-ounce mixture of red and gold beads that she can sell for $2 an ounce. the solution of the system shows the number of beads needed for juanita to break even. x + y = 12, x + 3y = 24 how many ounces of red beads will juanita buy to break even? how many ounces of gold beads will she buy?

Can someone me out here and the tell me the greatest common factor

21 a stick 7 inches long is broken into two pieces, so that one piece is twice as long as the other one. how long are the two pieces?