Question

1. The Enormous State University History Department offers three courses—Ancient, Medieval, and Modern History—and the chairperson is trying to decide how many sections of each to offer this semester. The department is allowed to offer 45 sections total, there are 5,200 students who would like to take a course, and there are 61 professors to teach them. Sections of Ancient History have 100 students each, sections of Medieval History hold 50 students each, and sections of Modern History have 200 students each. Modern History sections are taught by a team of two professors, while Ancient and Medieval History need only one professor per section. How many sections of each course should the chair schedule in order to offer all the sections that they are allowed, accommodate all of the students, and give one teaching assignment to each professor? HINT [See Example 2.] (Assume each section has the maximum number of students allowed.)

Ancient History __ sections

Medieval History __ sections

Modern History __ sections

2. Inverse mutual funds, sometimes referred to as "bear market" or "short" funds, seek to deliver the opposite of the performance of the index or category they track, and can thus be used by traders to bet against the stock market. This question is based on the following table, which shows the performance of three such funds as of February 27, 2015.

	Year-to-date Loss
SHPIX (Short Smallcap Profund)	4%
RYURX (Rydex Inverse S&P 500)	3%
RYCWX (Rydex Inverse Dow)	6%

You invested a total of $11,000 in the three funds at the beginning of 2015, including an equal amount in RYURX and RYCWX. Your year-to-date loss from the first two funds amounted to $290. How much did you invest in each of the three funds?

SHPIX $__

RYURX $__

RYCWX $__

Answer 1

1)

Let

x= No of section in ancient history

y= No of section in Mediviel

Z= No of section in Modern History

Total No Of Students = 5200

Total No of Sections =45

Total no of Professors=61

No OF students Per section:

100,50&200 in ancient ,mediviel,and modern history section per section Respectively, hence we could say

100x + 50y + 200z = 5200 (1)

No of Professors needed per section:

1,1&2 in ancient ,mediviel,and modern history section per section Respectively, hence we could say

x + y + 2z = 61 (2)

& x+ y+ z =45 (3)

Solving equation 2&3 b elimination method

    x + y + 2z = 61

    x+ y+ z =45   

- - - -

z=16

Solving equation 1&2(multiply equation 2by 100) elimination method:

100x + 50y + 200z = 5200

100x +100y+200z=6100

- - - -

y=18

putting z and y in euation 3  

   x+ y+ z =45

x =11

Hence No of Sections in

ancient history = 11

medieval History =18

Modern History =16

  

2) Let X be the investment in SHPIX

y be the investment in RYURX

z be the investment in RYCWX

As Investment in RYURX and RYCWX are same we can consider y=z

and

x + y+ y = 11000

ie x + 2y = 11000 (1)

As total loss from Both x(being 4% individually) and y (being 3% individually) is 290$ that means

.04x + .03y = 290 (2)

By Multiplying equation 1 with .04 and equation 2 with 1 we get:

.04x + .08y = 440

.04x+ .03y = 290

- - -

by elimination method investment in y is 3000 = investment in z= 3000

and investment in x = 5000

HEnce investment in SHPIX = 5000$

  investment in RYURX = 3000$

investment in RYCWX = 3000$