<ol>
<li><p>We can actually solve this without finding an equation for f(x) Note that 7 is halfway between 2 and 12. Since f(x) is linear, we expect f(7) to be halfway between f(2) and f(12), which is (7+1)/2 = 4, (D).</p></li>
<li><p>The volume of the first cylinder is 16<em>9</em>pi. The volume of the second cylinder is 81<em>h</em>pi, where h is the second cylinder’s height. Assume that the two volumes are equal, since we want to minimize h. Then</p></li>
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<ol>
<li>We could set up a system of equations, which definitely works, but in this case there is a slightly faster solution. Note that the average price per ticket is $700/200 = $3.50. This same ratio occurs when we buy 1 children’s ticket and 3 adult tickets (since 1 child/3 adults cost $14, $14/4 = $3.50). Indeed, it can be checked that 50 children’s tickets and 150 adult tickets were sold, so the ratio is 1:3, (B).</li>
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<p>For 3, using a graphical ratio is actually my favorite way to solve similar problems. It is based on moving averages. Easy to do but … harder to explain! </p>
<p>Getting to the 3.5 is indeed the key. After that write down something like.</p>
<p>2.00 (x x x) 3.50 (x) 4.00</p>
<p>All x represent .50 and you simply count them. 3 to 1 is the answer</p>
<ol>
<li>I do this kind of questions in this way:</li>
</ol>
<p>f(x) = #</p>
<p>f(x) is x</p>
<h1>is y</h1>
<p>(2,7) and (12,1)
a) Find slope (y2-y1)/(x2-x1) ( its -3/5)
b) Plug in either (2,7) or (12,1) into this equation y=mx+b which tells you that b is 8.2
c) Since you have f(7), x is 7. Find y
d) y=7(-3/5) + 8.2
ans. 4 (D)</p>
