Week 8 HW - Algebra Part II

Name: ______January 12, 2017

  1. If a = 2, b = 1, and c = 0, what is the value of 2a + 3b + 5c?
  1. For what value of x is the following equation true?

3 =

  1. The area of a square is 36 square centimeters. A rectangle has the same perimeter as the square. The length of the rectangle is twice its width. What is the area of the rectangle in square cm?
  1. Ron and Harry start with the same number of Chocolate Frog trading cards. After Ron gives 12 of his cards to Harry, Harry then has two times as many cards as Ron does. How many cards did Ron have at the start?
  1. Toni picks a number and multiplies it by 3. She then adds 4 to the result and finally divides this new number by 2. Her final result is 14. With what number did she start?
  1. Jessie has $5.10 worth of stamps. She has equal numbers of 50-cent, 20-cent, 10-cent and 5-cent stamps. She has no other stamps. How many 50-cent stamps does she have?
  1. The Seahawks beat the Steelers in a football game. The sum of their scores was 44. The difference of their scores was 20. How many points did the Seahawks score?
  1. A mystery number was decreased by 8, then tripled, followed by six doublings, resulting in the number 768. What is the mystery number?

BONUS PROBLEMS

  1. If r – s = 1 and 2r + 3s = 32, what is the value of the expression r + 4s?
  1. Sherry has five times as many computer games as Jay. Nairan has three times as many computer games as Jay. Sherry has 16 computer games more than Nairan has. How many computer games does Jay have?
  1. Admission to the local movie theater is $3 for each child and $7 for each adult. A group of 12 people pays $64 admission. How many children are in this group?
  1. Every weekend, Mary dedicates all her spare time to her favorite singer, Justin Bieber. This past Saturday, she spent 84 minutes listening to her favorite Justin Bieber song 20 times in a row and pasting 24 Justin Bieber photos in her scrapbook. On Sunday, she took 62 minutes to listen to the same song 10 times in a row and paste 32 photos in her scrapbook. Assuming Mary spends the same amount of time pasting each photo in her scrapbook, and that she doesn’t paste and listen to the song at the same time, how long does it take Mary to listen to her favorite song?

SOLUTIONS:

  1. 7

2a + 3b + 5c = 2(2) + 3(1) + 5(0) = 4 + 3 + 0 = 7.

  1. x = 10

Multiplying both sides by 4 we get 12 = x + 2. Subtracting 2 from both sides, we get x = 10.

  1. 32 sq. cm.

Since the area of the square is 36, each side must be 6, giving it a perimeter of 24. Let the width of the rectangle = x. Then the length of the rectangle = 2x. So x + 2x + x + 2x = 24, 6x = 24, x = 4. Then the width of the rectangle is 4 and the length is 8, giving it an area of 32 sq. cm.

  1. 36 cards

Since Ron gives 12 cards to Harry, let each start with x + 12 cards. Then, when Ron gives the cards to Harry, he then has x, while Harry has x + 24. Since x + 24 = 2x, x = 24. Therefore, Ron started with 24 + 12 cards, or 36.

  1. 8

Let the number = x. Step one, she multiplies it by 3: 3x. Then she adds 4 to the result: 3x + 4. Then she divides that result by 2: . The final result = 14, so = 14. Multiplying both sides by 2, we get 3x + 4 = 28. Subtracting 4 from both sides, 3x = 24; dividing both sides by 3, x = 8.

  1. Six 50-cent stamps

Since Jessie has the same number of each kind of stamp, we can use x to represent the number of stamps in each denomination. So 50x + 20x + 10x + 5x = 510. Solving for x: 85x = 510; dividing both sides by 85, x = 6.

  1. 32 points

Let x = the Seahawks and y = the Steelers. x + y = 44, and x – y = 20. Adding the two equations together, we get 2x = 64, so x = 32.

  1. 12

(3) (x - 8) (2) (2) (2) (2) (2) (2) = (3) (x – 8) (64) = (192) (x – 8) = 192x – 1536 = 768. Adding 1536 to both sides, 192x = 2304; dividing both sides by 192, x = 12.

  1. 31

Transposing, we know that r = s + 1. Substituting s+1 for r in the second equation, we get 2(s+1) + 3s = 32 or 5s + 2 = 32. Solving for s, 5s = 30, s = 6. Knowing s = 6, r = 7, so r + 4s = 7 + 24 = 31.

  1. 8 computer games

Let x = the number of computer games Jay has. Then Nairan has 3x computer games and Sherry has 5x computer games. We can also say that Sherry has 3x + 16 computer games. So 5x = 3x + 16, 2x = 16, and x = 8.

  1. 5 children

Let x = the number of children and y = the number of adults. x + y = 12, and 3x + 7y = 64. Multiplying the first equation by -3, we get -3x - 3y = -36. Adding that to the second equation, we get 0x + 4y = 28, therefore y = 7. Since y = 7, x = 5.

  1. 3 minutes

Let the length of the song = x and the amount of time to paste a photo = y. On Saturday, 20x + 24y = 84, and on Sunday, 10x + 32y = 62. Multiplying the first equation by -1/2, we get -10x - 12y = -42. Adding the two equations together, we get 20y = 20, therefore y = 1. Since y = 1, 20x + 24 = 84, solving for x, 20x = 60, and x = 3.

Cascade Ridge PTSA Math Club1Show your work on a separate sheet of paper.