PP1 (Shorter) Quant Section 1 (Medium) Q9

<p><span style="color:#27ae60;"><span style="font-size:20px;">Solving the Problem</span></span></p> <p>The problem informs us that the land will be subdivided into two lots: either $80$ or $100$ feet of lake frontage. The problem then informs us that $\frac{1}{9}$ of the lots are to have $80$ feet of lake frontage. From this piece of information, we can make a very important deduction:</p> <ul> <li><strong>Very important deduction</strong>: If $\frac{1}{9}$ of the lots have $80$ feet of lake frontage, and there are only two possible lots, then $1 - \frac{1}{9} = \frac{8}{9}$ of the lots must have $100$ feet of lake frontage.&nbsp;</li> </ul> <p>This is a good start, but we still don&#39;t know how many lots have $80$ feet of lake frontage and how many have $100$ feet. If we say that the total number of lots is $a$, then we can set up the following equation:</p> <p style="text-align: center;">$$x = \frac{1}{9}a \times 80 + \frac{8}{9}a \times 100$$</p> <p>The next piece of information from the problem allows us to crack the puzzle and solve for the total number of lots, $a$. It says the &quot;remaining 40 lots are to have $100$ feet of lake frontage each.&quot; Ahh, so $\frac{8}{9} \times total = 40$. Solving for the total, $a$, we calculate $a$ to be $45$ lots.&nbsp;&nbsp;</p> <p style="text-align: center;">$$x = \frac{1}{9}45 \times 80 + \frac{8}{9}45 \times 100$$</p> <p style="text-align: center;">$$x = (5)(80) + (40)(100)$$</p> <p style="text-align: center;">$$x = 400 + 4000$$</p> <p>Thus, <strong><span style="color:#27ae60;">the correct answer is D, ($4$,$400$)</span></strong>.</p>