Math HW 2 1) In the 2000 census, Georgia had 3 as many people as Illinois (U.S. Bureau of Census, ). If the population of Georgia was 8 million, then what was the population of Illinois? 2) With AT&T's One Rate plan you are charged 5 cents per minute plus $2.95 for long-distance service for one month. If a long-distance bill is $4.80, then what is the number of minutes used? 3) Olivia got a 6% discount when she bought a new Xbox. If she paid $399.50 and x is the original price, then x satisfies the equation x − 0.06x = 399.50. Solve the equation to find the original price. 4) What was the original price of a stereo that sold for $560 after a 20% discount? 5) The sum of three consecutive integers is 48. Find the integers. 6) The length of a rectangular piece of property is 1 foot less than twice the width. If the perimeter is 748 feet, find the length and width. 7) The angle formed by the guy wire and the ground is 3.5 times as large as the angle formed by the guy wire and the antenna. Find the degree measure of each of these angles. 8) Bridgette drove her car for 2 hours on an icy road. When the road cleared up, she increased her speed by 35 miles per hour and drove 3 more hours, completing her 255-mile trip. How fast did she travel on the icy road? 9) Pierce drove from Allentown to Baker, averaging 55 miles per hour. His journey back to Allentown using the same route took 3 hours longer because he averaged only 40 miles per hour. How long did it take him to drive from Allentown to Baker? What is the distance between Allentown and Baker? 10) Ralph got a 12% discount when he bought his new 2010 Corvette Coupe. If the amount of his discount was $6606, then what was the original price of the Corvette? 11) When Susan bought her new car, she also got a discount of 12%. She paid $17,600 for her car. What was the original price of Susan's car? 12) Sarah is selling her house through a real estate agent whose commission rate is 7%. What should the selling price be so that Sarah can get the $83,700 she needs to pay off the mortgage? 13) Ruth Ann invested some money in a certificate of deposit with an annual yield of 9%. She invested twice as much in a mutual fund with an annual yield of 10%. Her interest from the two investments at the end of the year was $232. How much was invested at each rate?
 

Math hw

 

1. In 2000 census, Georgia had 23

   

    as many people as Illinois (U.S. Bureau of Census, www.census .gov). If the population of Georgia was 8 million, then what was the population of Illinois?

Let Illinois have x population.

2x/3 = 8 million

x = 8*3/2 =12 million

2.  With AT&T's One Rate plan you are charged 5 cents per minute plus $2.95 for long-distance service for one month. If a long-distance bill is $4.80, then what is the number of minutes used?

Let the minutes be x.

0.05x+2.95 = 4.8

0.055x =4.8-2.95 =1.85

x = 1.85/0.05 =37 minutes

3. Olivia got a 6% discount when she bought a new Xbox. If she paid $399.50 and x is the original price, then x satisfies the equation x − 0.06x = 399.50. Solve the equation to find the original price.

Let original price be x.

x − 0.06x = 399.50

0.94x = 399.50

x = 399.50/0.94 = $425

4. What was the original price of a stereo that sold for $560 after a 20% discount?

Let the price be x.

x - 0.2x = 560

0.8x = 560

x = 560/0.8 =$700

5. The sum of three consecutive integers is 48. Find the integers.

Let the integers be x-1, x, x+1.

 x-1 + x + x+1 =48

3x = 48

x = 16

So integers are 15, 16, 17.

6. The length of a rectangular piece of property is 1 foot less than twice the width. If the perimeter is 748 feet, find the length and width.

Let width be b.

l =2b-1

perimeter = 2(l+b)

748 = 2*(2b-1 +b)

374 = 3b -1

3b =375

b = 375/3 =125 foot

l = 2*125 -1 = 249 foot

7. The angle formed by the guy wire and the ground is 3.5 times as large as the angle formed by the guy wire and the antenna. Find the degree measure of each of these angles.

Let angle between guy wire and ground is 3.5 x, angle between guy wire and the antenna x.

3.5x+x = 90

4.5x =90

angle between guy wire and the antenna ,x =20 degrees

angle between guy wire and ground ,3.5 x =75 degrees

8. Bridgette drove her car for 2 hours on an icy road. When the road cleared up, she increased her speed by 35 miles per hour and drove 3 more hours, completing her 255-mile trip. How fast did she travel on the icy road?

Let the initial speed in icy road be x miles per hour.

2x+3(x+35) = 255

5x + 105 = 255

5x = 150

x =150/5 = 30 miles per hour.

9.  Pierce drove from Allentown to Baker, averaging 55 miles per hour. His journey back to Allentown using the same route took 3 hours longer because he averaged only 40 miles per hour. How long did it take him to drive from Allentown to Baker? What is the distance between Allentown and Baker?

Let initial driving time be x hours.

55*x = 40 (x + 3)

55x -40x = 120

15x = 120

x = 120/15 = 8 hours

He drove from Allentown to Baker in 8 hours and opposite direction in 11 hours.

10.  Ralph got a 12% discount when he bought his new 2010 Corvette Coupe. If the amount of his discount was $6606, then what was the original price of the Corvette?

Let original price be x.

0.12 x =6606

x = 6606 /0.12

x = $55050

11.  When Susan bought her new car, she also got a discount of 12%. She paid $17,600 for her car. What was the original price of Susan's car?

Let original price be x.

 x − 0.12x = 17600

0.88x = 17600

x = 17600/0.88 = $20000

12. Sarah is selling her house through a real estate agent whose commission rate is 7%. What should the selling price be so that Sarah can get the $83,700 she needs to pay off the mortgage?

Let x be the selling price.

x – 0.07 x =83700

0.93x = 83700

x = 83700 / 0.93

x = $90000

13.  Ruth Ann invested some money in a certificate of deposit with an annual yield of 9%. She invested twice as much in a mutual fund with an annual yield of 10%. Her interest from the two investments at the end of the year was $232. How much was invested at each rate?

Let Ruth Ann invested x amount in a certificate of deposit so, Ruth invested 2x in mutual fund.

x * 0.09 + 2x *0.10 = 232

0.09x+0.2x = 232

0.29 x = 232

x =232/.29 = $800

So Ann invested $800 in a certificate of deposit with an annual yield of 9% and 1600 in mutual fund with an annual yield of 10%.