Math questions

<p>Here's a link to my questions
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<ol>
<li>There can be 2 boxes with red scarves, 2 with brown, 2 yellow, and 2 grey for a total of 8 boxes. So we can elimiinate choices (A) through (D). This leaves choice (E) as the answer.</li>
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<p>Note: If you add a ninth box, it must contain either a red, brown, yellow, or grey scarf, ensuring that there are 3 boxes with scarves of the same color.</p>

<ol>
<li>Redraw the given picture twice, one directly above the other. Now on the top one darken the ray AC (start at A and keep going right). On the bottom one darken ray BA (start at B and keep going left. The intersection is the set of points common to both. To see this visually draw two vertical lines, one through A, and one through B. We now see tha the answer is segment AB, choice (B).</li>
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<ol>
<li>Let’s start with choice (C) as our first guess. So we are guessing that there are 160 books. To find the number of students in the class we divide 140 by 4 to get 140/4 = 35 students (we are subtracting 20 before dividing because there are 20 books left over). Now, 3 students do not take a book. Therefore 32 students take 5 books each. 32*5 = 160. This is correct. So the answer is choice (C).</li>
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<ol>
<li>Algebraic solution (not recommended): Let x be the number of students in the class, and b the number of books. Then (b - 20)/4 = x, and 5(x - 3) = b.</li>
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<p>This becomes:</p>

<p>b - 20 = 4x and 5x - 15 = b.</p>

<p>b = 5x - 15
b = 4x + 20</p>

<p>Subtracting the 2 equations gives 0 = x - 35, or x = 35.
Substituting x = 35 into the second equation (we can actually use either one) gives
b = 4*35 + 20 = 140 + 20 = 160, choice (C).</p>