<PRE><B>Question 1203745</B>
&lt;pre&gt;
A man has $250,000 invested in three properties. One earns 12%, one 10% and one 8%. His annual income from the properties is $23,900 and the amount invested at 8% is twice that invested at 12%.
(a) How much is invested in each property?
12%property			$ 
10%property			$ 
8%property			$ 


(b) What is the annual income from each property?
12%property			$ 
10%property			$ 
8%property			$ 

Let amount invested in the property earning 12%, be T
Then amount invested in the property earning 8% = 2T
So, amount invested in the property earning 10% = 250,000 - (T + 2T) = 250,000 - 3T

Income from property earning 12%: .12T
Income from property earning 8%: .08(2T) = .16T
Income from property earning 10%: .1(250,000 - 3T) = 25,000 - .3T

Since total income from the 3 investments is $23,900, we get: .12T + .16T + 25,000 - .3T = 23,900
                                                                       .12T + .16T - .3T = 23,900 - 25.000
                                                                                  - .02T = - 1,100 
    &lt;font color = red&gt;&lt;font size = 3&gt;&lt;b&gt;Amount invested in property earning 12%&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;, or {{{highlight_green(matrix(1,9, T, &quot;=&quot;, &quot;- 1,100&quot;/(- .02), &quot;=&quot;, &quot;- 110,000&quot;/(- 2), &quot;=&quot;, &quot;110,000&quot;/2, &quot;=&quot;, highlight(&quot;$55,000&quot;)))}}}

                         &lt;font color = red&gt;&lt;font size = 4&gt;&lt;b&gt;Amount invested in property earning 8%:&lt;/font&gt;&lt;/font&gt;&lt;/b&gt; 2T = 2(55,000) = &lt;font color = red&gt;&lt;font size = 4&gt;&lt;b&gt;$110,000&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;

  &lt;font color = red&gt;&lt;font size = 2&gt;&lt;b&gt;Amount invested in property earning 10%:&lt;/font&gt;&lt;/font&gt;&lt;/b&gt; 250,000 - (55,000 + 110,000) = 250,000 - 165,000 = &lt;font color = red&gt;&lt;font size = 4&gt;&lt;b&gt;$85,000&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;

Income from property earning 12%, property earning 8%, and property earning 10% are: .12T, .16T, and 25,000 - .3T,
respectively. Use those facts, along with T being $55,000, to find the income from each of the 3 properties.&lt;/pre&gt;</PRE>