1. If 5 times the value of a number is increased by 3, the result is 28. What is the number?
5x+3=28
5x=25 x=5 The answer is 5
2. If 4 times the reciprocal of a number is 3 more than 5/2 times the reciprocal of that number, find the number.
4*(1/x)=(5/2)*(1/x)+3
4/x=(5/2x)+3
(8/2x)=(5/2x)+3
(8/2x)-(5/2x)=3
(3/2x)=3
x=1/2
The answer would be x=1/2
3. John had $30,000 to invest. He invested part of this money in bonds paying 12% annual simple interest and the rest of the money in a savings account giving 4% annual interest. At the end of the year, he received $2,400 as extra income. How much money did John place in each investment?
.4x+.12(30000-x)=2400
.04x+.12(30000)-.12x=2400
.04x+3600-.12x=2400
.12x-.04x+3600=2400
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The length of a rectangular field is 50 feet less than its width. If the perimeter of the field is 840 feet, find the length of the field
2x+2y=840
2(y-50)+2y=840
2y-100+2y=840
4y=940 y=235 x=235-50 x=185 The length of the field would be 185Ft.
11. Alan participated in a car race in which he had to cover a distance of at least 50 kilometers. He had fuel in his car for a maximum distance of 53 kilometers. If the distance is given by , where t is the time in hours, find the minimum and maximum number of hours for which Alan can drive his car. for at least 50 km s (t)=3t+47 s (t) =50
50=3t+47
3t=3 t=1 hour for a maximum of 53 km s(t)=53 53=3t+47
3t=6
t=2 hours
The minimum number of hours which Alan can drive is 1 hour. the maximum Alan can drive is 2hours.
12. in a 2-digit number, the number in the unit’s place is 4 more than the number in the ten’s place. If the digits of the number are reversed, the new number is 6 more than thrice the original number. Find the original number.
13.
x= units digit y=tens digit
10x+y=3(10y+x)+6
7x-29y=6
7(y+4)-29y=6
7y+28-29y=6
-22y=-22
y=1
Therefore x=5
Therefore the original number is
Question 8: At night, a driver should dim his headlights when an oncoming motor vehicle comes within:
Beverly and Kyle Nelson currently insure their cars with separate companies paying $450 and $375 a year. If they insure both cars with the same company, they would save 10 percent on the annual premiums. What would be the future value of the annual savings over ten years based on an annual interest rate of 6 percent?
You can earn 5% per year compounded annually for the next 4 years, followed by 8% per year compounded quarterly for 5 years. What is the average annual compounded rate of return over the 9 year period?
Casey took 25 tests in 135 days. At this rate, in how many days will she take another 10 tests?
(3 marks) c) Determine the optimal number of bus and train travelers. (2 marks) d) Say a train strike significantly reduced the number of trains available. By how much would the train capacity constraint have to fall for the optimal solution to be altered? (2 marks)
b. Determine the two product numbers with the largest total dollar sales for subsequent follow-up to verify the selling prices and quantities shipped.
In a right triangle, the base is of the height. The area is 150. What is the length of the hypotenuse?
Two numbers have a sum of 20. The sum of their squares is a minimum.
16. 30 acres of cotton uses water at the rate of 0.21 inches per day. How many cubic feet per day does the cotton use?
Now I have to figure out a minimum or maximum allowance of cargo to be found. The Burbank Buy More is going to make an order which will include, at most, 60 refrigerators. What is the maximum number of TV’s that could also be delivered on the same truck? To find the answer, I will plug 60 into the x place of my inequality and solve for y.
9. You want to purchase a business with the following cash flows. How much would you pay for this business today assuming you needed a 14% return to make this deal?
3. If the load factor could be increased to 75 percent, how many passenger train cars must be operated to earn pre-tax income of $
14) Consider the following transshipment problem. The shipping cost per unit between nodes 1 and 2 is $10, while the shipping cost per unit between nodes 2 and 3 is $12. What is the objective function?
Each week there are 300 pounds of material 1; 400 pounds of material 2; and 200 hours of labor. The output of product A should not be more than one-half of the total number of units produced. Moreover, there is a standing order of 10 units of product C each week.