Question 1

A flower border of uniform width is to be added to a rectangular lawn,30 feet by 40 feet.How wide should the border be so that 600 sq ft of lawn remains?

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Question 2

Suppose consumers purchase q units of a manufacturer's product when the price per unit (in dollars)is  If no more than 75 units can be sold,then the number of units that must be sold in order that sales revenue be $1000 is
A) 20.
B) 25.
C) 40.
D) 50.
E) 75.

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Question 3

An electric utility company is going to locate its new power plant along a straight road connecting the towns of Exton and Whyton,which are 10 miles apart.For political reasons,the utility company will buy coal from both towns.The price of coal per ton from Exton is $72.65 plus $0.45 per mile for delivery.The price per ton from Whyton is $72.25 plus $0.25 per mile for delivery.How far (in miles)from Exton should the plant be located if the price of coal per ton delivered from Exton is to be equal to that from Whyton? (Hint: If d is the distance of the plant from Exton,then 10 - d is the distance from Whyton.)
A) 2 
B) 3
C) 3 
D) 4
E) 6

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Question 4

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?

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Question 5

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?
A) 50%
B) 60%
C) 65%
D) 70%
E) 80%

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Question 6

A bank loaned $3320 to a company for the development of two products.If the loan for product A was $1520 more than the other,how much was loaned for each product?

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Question 7

A baker must prepare 6 cups of pie filling.The recipe calls for  
cup of sugar for each 4 cups of fruit.How much of each ingredient should be used?

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Question 8

A metallurgist is preparing 63 kg of an alloy.It must consist of 3 parts aluminum and 4 parts copper.How much of each metal should be used?

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Question 9

A rectangular field is twice as long as it is wide.Find the dimensions of the field if it needs 600 feet of fencing to go around the field.

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Question 10

The sum of 3 integers is 27.The second is 3 more than the first,and the third is two more than twice the second integer.Find the three integers.

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Question 11

An elder brother is twice as old as his younger brother at the present.Six years ago the elder brother was three times as old as the younger brother.Find the present age of the brothers.

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Question 12

The sum of two real numbers is 12.The sum of their reciprocals is  
.Find the two numbers.

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Question 13

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

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Question 14

A chemist must prepare 540 ml of a chemical solution.It is to be made up of 4 parts acid and 5 parts distilled water.How much of each should be used?

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Question 15

A homeowner needs to make a cover for a circular pool with a diameter of 18 feet.How much cover fabric should be ordered if the cover must extend 2 feet beyond the edge of the pool? (Hint: The area A of a circle is  
,where r is the radius.Assume π = 3.14,and round to the nearest square foot.)

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Question 16

A company will enclose a rectangular area of 12,800 square feet in the rear of its plant.One side will be bounded by the building and the other three sides by fencing.Suppose that 400 feet of fencing will be used and that the side of the building has a length of 100 ft.What will be the dimension (in feet)of the side of the rectangle that is opposite the building?
A) 20
B) 40
C) 60
D) 80
E) 90

Accepted Answer

The total perimeter of the rectangle is the sum of the three sides of fencing plus the side of the building that is already there. Since one side is the building, and it's 100 feet, and we have 400 feet of fencing for the other three sides, the total perimeter is 400 + 100 = 500 feet. If we let x be the length of the two sides that are fenced (not the side opposite the building), then the equation for the perimeter is 2x + 100 + side opposite the building = 500. The side opposite the building is also 100 feet because it's parallel to the side of the building, making the equation 2x + 200 = 500. Solving for x gives x = (500 - 200) / 2 = 150 / 2 = 75 feet for each of the two sides. However, the question asks for the dimension of the side opposite the building, which is 100 feet, matching option D.

Question 17

A rectangular deck attached to a ski lodge is 22 m long and 10 m wide.Planter boxes will be added along the 3 open sides,which include 1 long side and both short sides.How wide can the boxes be to leave 180 sq m of deck space?

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Question 18

A company produces and sells q units of its product.If the variable cost is $4/unit,fixed costs are $4800 and the selling price is $28/unit,find the number of units the company must produce to split even (i.e.,zero profit).

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Question 19

A person wishes to deposit a total fo $10,000 in two accounts.The savings account pays yearly interest of 4% and fixed certificates of deposit pay a yearly interest rate of 7%.How much should the person deposit in each account so that he gets a total of $502 interest at the end of the year?

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Question 20

Imperial Educational Services (I.E.S.)wants to offer a workshop in pollution control to key personnel at Acme Corporation.I.E.S.will offer the course to thirty persons at a charge of $50 each.Moreover,I.E.S.will agree to reduce the charge for everybody by $1.00 for each person over the thirty who attends,up to a total group size of fifty.It has been determined that the greatest revenue the I.E.S.can receive is $1600.What group size will give this revenue?
A) 34
B) 36
C) 40
D) 44
E) 48

Accepted Answer

Let x be the number of participants over 30 who attend the workshop.

The revenue for the workshop can be expressed as:

R(x) = (30 + x)(50 - x)

where 50 - x represents the reduced charge per person attending.

We want to find the group size that will give us the greatest revenue, which is equivalent to finding the maximum value of R(x).

Expanding R(x), we get:

R(x) = -x^2 + 20x + 1500

Taking the derivative of R(x) with respect to x and setting it equal to 0 to find the critical point(s):

R'(x) = -2x + 20 = 0

x = 10

We can confirm that this is a maximum point by checking that the second derivative of R(x) evaluated at x = 10 is negative (-2).

Therefore, the optimal group size is:

30 + x = 30 + 10 = 40

So the answer is (C) 40.

Quiz 2: Applications and More Algebra