Hey, there, Brooklyn! For the first problem, set up a proportion. Think of the line that separates the numerator and denominator is the word 'per'. If it's 0.75 yd per costume, then your fraction is [tex]\frac{0.75(yards)}{1(costume)}[/tex]. If she buys 6 yards, simply multiply [tex]6 * 0.75[/tex], which is 4.5. However, making 4.5 costumes doesn't sound too possible, does it? It's better to just say she can make 4 costumes.
Now let's look at the second problem. If just one side has a length of [tex](4x - 2y)[/tex], then that means there must be another side with the same length, as it is a rectangle we're talking about here. That means we should multiply the known length by two and subtract it from the perimeter like this:
[tex]12x + 8y - 2(4x - 2y)[/tex]
Remember the PEMDAS method. Distribute the 2;
[tex]12x + 8y - 8x + 4y[/tex]
Now combine like terms: [tex]12x - 8x + 8y + 4y[/tex]
--> 6x + 12y
Now we have an answer, but it's not the right one. You see, this is the length of both of the unknown lengths. To get the right answer, divide this by 2. The other side is [tex]3x + 6y[/tex] units long. Hope this helped.
