<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 fraction of the new mixture is yellow dye?</p>
<p>Why can't you just add 2 and 1 then divide by 8 (the total parts)?</p>
<p>Because the question explicitly states that “equal amounts” of orange and green dye need to be mixed. In this case half of the mixture would contain Orange dye and half, green. You need to set up an equation accordingly.</p>
<p>Another way to solve this question would be to assume that each part of the mixture amounts to 10, for example. Now in orange, out of 10, yellow would equal 4 according to the ratio. In Green, yellow would equal 3.334 (10/3) according to the ratio.
When you add the two total (10+10) equal amounts up, you get 20. Out of that total of 20, the amount of yellow is (4+3.334=7.334).
So, (4+10/30)/20= 11/30</p>
<p>I hope that’s understandable. :)</p>
<p>I got 11/30 (did it in my head)</p>
<p>3x(3:2)=(9:6)
5x(2:1)=(10:5)</p>
<p>(11:9+10+5+6)
11/30</p>