Don't get this math MC

Test Preparation SAT Preparation
1

<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>

<li>3 over 16</li>
<li>1 over 4</li>
<li>11 over 30</li>
<li>3 over 8</li>
<li>7 over 12</li>
</ol>

<hr>

<h1>Here’s Why:</h1>

<p>Suppose that x quarts of the final mixture of dye will be made. Since it is to be made from equal amounts of orange and green dye, it will consist of 1 over 2x quarts of orange dye and 1 over 2x quarts of green dye. Since the orange dye has 2 parts yellow dye for each 5 parts total dye, 2 over 5 of it is yellow dye. Similarly, 1 over 3 of the green dye is yellow dye. The amount of yellow in the final mixture is given by</p>

<p>(2 over 5)(1 over 2)x + (1 over 3)(1 over 2)x = 1 over 5x + 1 over 6x</p>

<p>= 11 over 30x quarts</p>

<p>So 11 over 30 of the final mixture is yellow dye.</p>

<p>Note: Although “quarts” were used to express the amount of the final mixture, it could have been pints or any other unit of liquid measure.</p>

<p>Why can’t you just add the yellow parts (3) and write over the total number of parts (8)?</p>

2

<p>The question specifies that equal amounts of green and orange are mixed. Using your method, you’d be mixing 5 parts of orange dye (3 red, 2 yellow) against only 3 parts of green dye (2 blue, 1 yellow). Clearly these amounts are unequal, which is why your solution won’t give you the right answer. </p>

<p>All you need to do is standardize the amount of green and orange dye and you’ll be fine.</p>

3

<p>If you want a good shot at a perfect score for anything, you do it by overpreparing.</p>

4

<p>Thanks, javademon! Haha, I should have noticed that.</p>

5

<p>Look, Ma, no fractions (almost)!</p>

<p>If we mix 15 quarts of an orange (R:Y=3:2=9:6) dye and 15 quarts of a green (B:Y=2:1=10:5) dye, we’ll have 6+5=11 quarts of a yellow dye in 30 quarts of mixture.
11 : 30</p>