help me with this math question !!

Test Preparation
1

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<p>On the number line above, a and b represent distances between numbers as shown. If the ratio of a to b is 1 to 6, what is the value of b?</p>

<p>(A) 42
(B) 48
(C) 54
(D) 60
(E) 66</p>

2

<p>We need the number line diagram.</p>

3

<p><a href=“http://img14.imageshack.us/img14/4632/ciud.png[/url]”>http://img14.imageshack.us/img14/4632/ciud.png&lt;/a&gt;&lt;/p&gt;

4

<p>If a = k and b = k^2 - a = k^2 - k = k(k-1), and a/b = 1/6, then:</p>

<p>1/(k-1) = 1/6</p>

<p>k-1 = 6</p>

<p>k = 7</p>

<p>Plugging in for b gives you 7(6) or 42.</p>

5

<p>Ok I see it now. So because you see k and k^2, you have to start just plugging in numbers for k and checking. The ratio between the distances is 1 to 6, so you can skip smaller numbers. </p>

<p>Try 5. The ratio of 5 to (5^2 - 5) is 1:4. Nope.</p>

<p>The ratio of 6 to (6^2 - 6) is to 1:5. Almost.</p>

<p>Ratio of 7 to (7^2 - 7) is 7:42, or 1:6. So k=7.</p>

<p>Now since b is essentially k^2 - k, we can plug in to get 7^2 - 7, or 42 (A).</p>