<p>I am two questions away from a 800 on Math...</p>
<p>17) The surface of a 3-dimensional solide consists of faces each of which has the shape of a polygon. What is the least number of such faces that the solid can have?</p>
<p>18) At the party, there was one pizza for every 3 people, one salad for every 6 people, and one cake for every 8 people. If the total number of pizzas, salads, and cakes was n, then, in terms of n, how many people were at the party?</p>
<p>Thanks.</p>
<ol>
<li><p>The polygon with the least sides is a triangle. With an equilateral triangle, you can make a triangular-base pyramid (more precisely a tetrahedron). Anyway, as you can see in the word tetra-hedron the word tetra denotes four, which means that such a solid has four faces. Therefore the least number of faces is four.</p></li>
<li><p>Select the least common denominator for 3, 6, and 8. First, you factor each number.
You have 3, 3<em>2, and 2</em>2<em>2, respectively. Take the highest powers for each type of integral factors you can identify, and you have 2</em>2<em>2</em>3, so you come up with 24. Then you can infer that there must have been 8 pizzas, 4 salads, 3 cakes, which means that n = 8+4+3 = 15. compare 24 with n (= 15) and you have 8/5 * n as the number of people who participated in the party.</p></li>
</ol>
<ol>
<li></li>
</ol>
<p>The total number of cakes (c), salads (s), and pizzas (p) is n, so:</p>
<p>c + s + p = n</p>
<p>Let k represent the number of people at the party. If there are ‘p’ pizzas, there must be 3p people at the party because there is 1 pizza for every 3 people , ‘s’ salads, there are 6s people there, because there is a salad for every 6 people, etc. so:</p>
<p>3p = k
6s = k
8c = k</p>
<p>p = k/3 , s = k/6, c = k/8 and we know that p + s + c = n, so</p>
<p>k/3 + k/6 + k/8 = n<br>
15k / 24 = n<br>
24n/15 = k, </p>
<p>k = 8/5n</p>
<p>So the number of people, k, in terms of n, is 8/5n.</p>
<p>I hate how this question is worded though because the phrase “If the total number of pizzas, salads, and cakes was n” sounds like there is n pizzas, n salads, and n cakes… Typically poor SAT question wording.</p>
<p>Thank you very much. Here is another one.</p>
<p>Gift certificates were sold by an ice-cream parlor in the month of July. Each giftcertificate was worth either $2, $3, or $5. Twice as many $2 gift certificates were sold as $3 certificates, and twice as many $3 gift certificates were sold as $5 gift certificates. The total value of all the gift certificates sold was 57$. How many $3 certificates were sold in July?</p>
<p>Thanks.</p>
<p>Let ‘a’ represent the number of $2 cards, ‘b’ to represent the number of $3 cards, and ‘c’ represent the number of $5 dollar cards.</p>
<p>Twice as many $2 cards as $3 cards:</p>
<p>a = 2b</p>
<p>Twice as many $3 cards as $5 cards:</p>
<p>b = 2c</p>
<p>Total value of all cards is $57:</p>
<p>2a + 3b + 5c = 57,</p>
<p>4b + 3b + 2.5b = 57, 9.5b = 57, b = 6, number of $3 cards.</p>
<p>Thank you very much!!!</p>