Math+Trail+Summer+2011+Solutions

These are our possible solutions to the UCSD Math Trail Problems.
Problem 1 Solution by Theresa Dinh & Cristina Jimenez Answer: 3/5 or .6 Explanation: Use a ruler to measure the height of one step (18cm) and the width of that same step (30cm). Slope is rise over run (height over width), so 18cm/30cm, which simplifies to 3/5 or .6. Some interesting considerations: We assumed the width and height of each step were the same for the whole staircase, so calculating one step's height and width would lead to the same slope as measuring the height and width of the whole staircase (because the measurements would be proportional). Secondly, because you are finding a ratio, it really doesn't matter if you use centimeters, inches, or some other random measurement (such as number of your thumb length); the units of measure cancel out when you do the proportion, so it yields the same simplified fraction.


 * Problem 3:** Solution by Rebecca Holland, Michelle Li, and Sonya Kuo
 * Answer:** 66,240 bricks on Library Walk
 * Explanation:** Library walk has a pattern of light and dark stripes. We counted the number of bricks in one stripe. We counted 30 bricks in a row and 12 rows in one stripe: 30 x 12 = 360 bricks in one stripe. Then we walked from one end of Library Walk to the other end, counting how many stripes are on Library Walk. We counted 184 stripes on Library Walk so we multiplied that number by 360 bricks per stripe to get a total of 66.240 bricks on Library Walk.


 * Problem 4 Solution** by Samantha Stanimirovich & Adrienne Villareal
 * Answer a.)** ~10 - 20 laps **b.)** 16 laps
 * Explanation:** Campus Loop is 4 miles long. Each lap around the track is equivalent to 1/4 miles, meaning 4 laps around the track equals 1 mile. So, 4 laps/mile x 4 miles = 16 laps around the track. The total number of laps around the track needed to equal the distance of Campus Loop is 16 laps.


 * Problem 5:** (Brynn Hewitt, Jessica Bell, Jason Jen)
 * Answer**: Approximately 1,023 feet long
 * Explanation**: We counted the number of sections that there are along library walk and found that there were 186. Then, we compared the height of one section to our height (by laying down across the section) to find out how long one section was. We found that they were each around 5 feet 6 inches long, so we multiplied the number of sections by the number of feet in one section to get the total number of feet. In other words: 186 sections * 5.5 feet per section = 1,023 feet total

Problem 2 Solution by Erik Marlin and Robert Tamayo Answer: ~1098ft. Explanation: There are 183 alternating sections of colored bricks, and each section is 12 bricks from south to north. Estimating the south/ north distance of the bricks as 6 in., you get 183 sections * 12 bricks/section * 1 ft./ 2 bricks = 1098ft.

a. There are 215 circles total and **5 circles** per plaque. b. If we divide 215 by 5 we can see that there are 43 “class of” plaques on library walk. Subtracting 43 from 2010, we see that the **class of 1967** was the first class to receive a plaque.
 * Problem 6 Solution - Allyson Chee, Claudia Pruitt, Victor Solis**

Example data: The ratio for male yogurt-eaters is 2:3, and for female yogurt-eaters, 4:1. If 50 men purchase yogurt throughout the day, we have to scale the ratio by 10, making it 20:30. For women, the ratio is also scaled by 10, making it 40:10. When you add up all the pink spoons distributed, you will find that 60 spoons are necessary. Since the cashier started the day with only 50 pink spoons, they will run out first.
 * Problem 7 Solution - Scott Frazier and Dana Leindecker**
 * || pink || blue ||
 * male || 2 || 3 ||
 * female || 4 || 1 ||

a. Assuming each window pane has equal width (which isn't true, but they are fairly similar), Geisel 7th and 5th floors more or less looks like this (units in windows): The area of this shape can be calculated as 352 - 4(92) + 4(42) = 965 OR 352 - 4(4*5+4*5+5*5) = 965
 * Problem 8 Solution - Chess Owen and Joe Cody**

So the area is 965 square windows. A window is approximately 6 ft wide, so (965 square windows)*(36 square ft)/(1 square window)=34740 square ft.