Why can you multiply both quantities in a ratio by the same number to find an equivalent ratio? Please help I have this for homework and I am very frustrated

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?

Two streets intersect at a 30- degree angle. at the intersection, the are four crosswalks formed that are the same length. what type of quadrilateral is formed by the crosswalks?

Which functions shave a maximum and are transformed to the left and down of the parent function ,check all that apply f(x) = x2? p(x) =14 (x+7)2 + 1