<h2>In the Barron, they told me to replace the variables with numbers as a tactic.</h2>
<p>If a = b + 1/2, b = 2c + 1/2, and c = 3d + 1/2, which of the following is an expression for d in terms of a?</p>
<p>A) (a - 2)/6</p>
<p>B) (2a - 3)/6</p>
<p>C) (2a - 3)/12</p>
<p>D) (3a - 2)/18</p>
<p>E) (4a - 3)/24</p>
<p>a - 0.5 = b
2c + 0.5 = a - 0.5
2c +1 = a</p>
<p>c = 3d + 0.5</p>
<p>2(3d + 0.5) + 1 = a
6d + 1 + 1 = a
6d + 2 = a
(a-2)/6 = d </p>
<p>A should be the answer! PM me if you have any questions. :)</p>
<p>Can you at least explain each steps you did there?!</p>
<p>Okay so this is basically a multi-step substitution problem.
You need to keep substituting stuff until you can get an equation with both a and d then solve for d. </p>
<p>a - 0.5 = b → first part of substitution… need to find out what b equals in terms of a so that I can use it for next equation.
2c + 0.5 = a - 0.5 → replace b with what b equals in terms of a so now I have an “a” and “c” equation.
2c +1 = a → simplified the previous equation. </p>
<p>c = 3d + 0.5 —> given equation </p>
<p>2(3d + 0.5) + 1 = a —> substitution yet again. since you know what c equals in terms of d, I just plugged it in to the second given equation so I now have an “a” and “d” equation.
6d + 1 + 1 = a → simplified above equation by distribution.
6d + 2 = a —> simplified above equation again
(a-2)/6 = d → isolated d </p>
<p>hopefully this brings some clarity to my work!</p>