Help with Alligation (spelling?)

Test Preparation
1

<p>The first question below, about the $3,000 and the interest. I cannot find help online, any help you can give me would be appreciated, I a frustrated! I seem to remember somrthjing about ratios but I havent been in school in years. </p>

<p>"Pat invests a total of $3,000, part of the money yields 10%/ year, the rest yields 8%/ year. If the total yearly interest from this is $256, how much of the money was invested at 10%? How much was invested at 8%?"</p>

<p>I figured out that 256/3000= total of 8.5% total return, so I am sure on a multiple choice exam, I could emiminate most of the choices, but that won't cut it. I want to know HOW to answer it and to apply the technique to other problems. I used to know how to do these (I think it was called alligation), but I cannot remember the details of the technique. Please help!</p>

2

<p>Let x be the amount that yields 10% per year. Therefore, the amount that yields 8% per year is (3000-x). </p>

<p>The total yearly interest is $256. This amount comes from 10% of x and 8% of (3000-x). So,</p>

<p>0.10x + 0.08 (3000-x) = 256
0.10x + 240 - 0.08x = 256
0.02x = 16
x = 800</p>

<p>So, the amount that yields 10% is $800, and the amount that yields 8% is (3000-800)=$2,200.</p>