Exam 2: Applications and More Algebra

An office complex consists of 300 units which rent at $760 per month with no vacancies.Each $20 per month increase will create four vacancies with no possibility of filling them.The owner wishes to receive $233,600 per month from the complex.How much should the rent be increased to meet this goal?

A group of biologists studied the nutritional effects on rats that were fed a diet containing 10% protein.The protein was made up of yeast and corn flour.By changing the percentage P (expressed as a decimal)of yeast in the protein mix,the group estimated that the average weight gain g (in grams)of a rat over a period of time was given by g = + 200P + 20.What percentage of yeast gave an average weight gain of 70 grams?

The cost of producing each copy of a travel guide is $0.95.It is sold to travel agents for $0.90 each,and the amount received for advertising is 10% of the amount received for all guides sold beyond 12,000.Find the fewest number of travel guides that must be sold to break even.

The cost of publishing each copy of a magazine is $1.75.The revenue from dealers if $1.60 for each copy.The amount received for advertising is 10% of the amount received for all magazines sold beyond 1,000.Find the smallest number of copies that must be sold to break even.

Solve: (1 - - 4(3 - ≥ 5

Evaluate:

A chef must prepare 10 cups of a sauce.The recipe calls for 1 part wine and 4 parts beef stock.How much of each ingredient should be used?

Solve: > 2

A company will manufacture a total of 5000 units of its product at plants A and B.At plan A the unit cost for labor and material combined is $2.50,while at plant B it is $3.00.The fixed costs at plant A are $6000 and at plant B they are $8000.Between the two plants the company has decided to allot no more than $28,000 for total costs.The minimum number of units that must be produced at plant A is

Evaluate:

A father wants to invest $50,000 in order to earn $4000 per year to help pay for his daughter's college education.He places $30,000 in a savings account earning 5% per year.He wants to place the rest of his investment in a mutual fund.How much will the mutual fund have to earn for him to make his goal?

The sum of two integers is 21.The second integer is three more than twice the first integer.Find both of the integers.

Solve: > 3

Evaluate:

The solution of < Is

A corporation plans to buy back some of its stock in 2 years for $1,081,600.It plans to invest $1,000,000 this year to have the necessary capital for this move.At what annual rate of interest,compounded annually,should it invest this million dollars to earn enough for its stock re-purchase?

Evaluate:

a = 4; r = 5

Hooke's Law of springs states that the force F (in pounds)required to stretch a spring x inches beyond its natural length is F = kx,where k is the "spring constant" for a given spring.If a certain spring has a spring constant k of 6.5 and 13 ≤ F ≤ 26,what are the corresponding values for x?

A fund is to be established to pay annual scholarships of $ 1,000,continuing forever.The first scholarship is payable in one years from now.If the annual rate of compound interest is 2.5%,find the value of the fund.