<p>Like many others I get the official SAT question of the day. There is this one that is from June 19th that I can't figure out. Seriously I always get the math ones right but this one is really hard and 70 percent of the people have missed it. </p>
<p>Can someone please explain the solution and how to get it. Their explanation still leaves me perplexed. By the way I put down D and it was the wrong answer. Here is the question:</p>
<p>QUESTION:</p>
<p>To make an orange dye, 3 parts of red dye are mixed with 2 parts of yellow dye. To make a green dye, 2 parts of blue dye are mixed with 1 part of yellow dye. If equal amounts of green and orange are mixed, what is the proportion of yellow dye in the new mixture?</p>
<p>SOLUTION:</p>
<p>Orange dye has total of 5 parts
Green dye has total of 3 parts</p>
<p>Since 15 is a multiple of both 3 and 5, let's mix 15 parts of EACH DYE together</p>
<p>That's 30 parts of total dye. For every 5 parts of orange dye, there are 2 parts yellow. There are 3 batches of 5-part orange dye. So out of the 30 part mixture there are 6 parts yellow. But this is from the Orange dye. For every 3 parts of green dye, 1 is yellow. There are 5 batches of 3-part green dye. So out of the 30 part mixture there are 5 MORE that are yellow.</p>
<p>6 + 5 = 11</p>
<p>Ans: 11/30</p>
<p>I got it right, but my logic is kinda weird. </p>
<p>I substituted Z for orange, X for Red, Y for Yellow, A for green, and B for Blue.</p>
<p>So for the first statement, Z=3x + 2y
and the second statement, A=2b + 1y</p>
<p>So then there are 5 parts in the first equation, and 3 parts in the second. So in the first equation, y is 2/5 of the total parts, and is 1/3 of total parts in the second equation. So the first mixture is 2/5 yellow dye and the second mixture is 1/3 yellow dye. To find the amount of yellow in the final mixture, I multiplied 2/5 x 1/3 each by 1/2, and then added them together, and that came out to 11/30.</p>
<p>ok this question seemed weird and i bumbled to the answer. Since we know the orange is made of 3r and 2y we consider that its 5 pieces. Then we say that G= 2B+y. Its clear to see that orange has 5 components and G has 3, so i just multipled the magnitude of each value in G by 5/3. Then when you add the 2y and the 5/3 y you get 11/3 y components out of the total of 10, since there are 5 for orange and 5 for green. (11/3)/10=11/30. Simular to amu. I wouldn't have figured this out on the SAT</p>
<p>Okay, there are some answers posted already, but here's my thinking.</p>
<p>You have </p>
<p>Orange = 3 red: 2 yellow
Green = 2 blue: 1 yellow</p>
<p>altogether, orange dye has 5 parts. Green dye has 3. In order to make them equal, find a common factor. I used 15. So you need to multiply all parts of the orange by 3 and all parts of the green by 5 so then each dye will have the same amount of parts.</p>
<p>so then you have orange = 9 red: 6 yellow, green = 10 blue: 5 yellow</p>
<p>Add up all the yellows you have over the total amount of dye and it's 11/30.</p>