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MATH Problems 1-15 I’ll have more problems up this weekend. 1. The weekly fee for staying at the Pleasant Lake Campground is $20 per vehicle and $10 per person. Last year, weekly fees were paid for v vehicles and p persons. Which of the following expressions gives the total amount, in dollars, collected for weekly fees last year? $ how many total $ vehicles $20 v 20v people $10 p 10p total t = 20v+10p 2. If r = 9, b = 5, and g = −6, what does (r + b − g)(b + g) equal? r b g b g 9 5 6 5 6 14 6 5 6 20 1 20 3. A copy machine makes 60 copies per minute. A second copy machine makes 80 copies per minute. The second machine starts making copies 2 minutes after the first machine starts. Both machines stop making copies 8 minutes after the first machine started. Together, the 2 machines made how many copies? 0 1st: 2nd: 1 60 3 2 60 4 6 5 7 8 60 60 60 60 60 60 Total 480 80 80 80 80 80 80 480 960 3b. A copy machine makes 60 copies per minute. A second copy machine makes 80 copies per minute. The second machine starts making copies 2 minutes after the first machine starts. Both machines stop making copies 8 minutes after the first machine started. Together, the 2 machines made how many copies? A Quicker Way (maybe) I like the first method many times because it helps me “get the feel of the problem”. 60 copies 80 copies 8 min 6 min min min 480 copies 480 copies 960 copies 4. Marlon is bowling in a tournament and has the highest average after 5 games, with scores of 210, 225, 254, 231, and 280. In order to maintain this exact average, what must be Marlon’s score for his 6th game? Games 1-5 Pins 1,200 Avg 240 4b. Marlon is bowling in a tournament and has the highest average after 5 games, with scores of 210, 225, 254, 231, and 280. In order to average 250, what must Marlon score on his last game? Games 1-5 6 6-game total Pins 1,200 ? 300 1,500 250 6 Avg 240 250 4b. Marlon is bowling in a tournament and has the highest average after 5 games, with scores of 210, 225, 254, 231, and 280. In order to average 250, what must Marlon score on his last game? A Quicker Way (maybe) I like the first method many times because it helps me “get the feel of the problem”. average 250 total count 1200 x 6 1500 1200 x 300 x 5. Joelle earns her regular pay of $7.50 per hour for up to 40 hours of work in a week. For each hour over 40 hours of work in a week, Joelle is paid 1½ times her regular pay. How much does Joelle earn for a week in which she works 42 hours? regular OT $ amt hours total 7.50 40 $300.00 2 $22.50 42 $322.50 7.501.50 11.25 total 5b. Joelle earns her regular pay of $7.50 per hour for up to 40 hours of work in a week. For each hour over 40 hours of work in a week, Joelle is paid 1½ times her regular pay. How much does Joelle earn for a week in which she works 42 hours? tot 7.508 11.25 2 300.00 22.50 322.50 5c. Joelle earns her regular pay of $7.50 per hour for up to 40 hours of work in a week. For each hour over 40 hours of work in a week, Joelle is paid 1½ times her regular pay. She owes her Dad $400. If she works 40 hours during the week, how long does she have to work on Saturday to repay her Dad? (assume she must work complete hours). 40 7.50 x 11.25 400.00 300 11.25x 400 11.25x 100 x 8.8 9hrs 6. Which of the following mathematical expressions is equivalent to the verbal expression “A number, x, squared is 39 more than the product of 10 and x” ? a number, x, squared is 39 more product of than the 10 and x x 39 10x 2 7. If 9(x − 9) = −11, then x = ? 9 x 9 11 9 x 81 11 81 81 9 x 70 9 9 x 70 9 8. Discount tickets to a basketball tournament sell for $4.00 each. Enrico spent $60.00 on discount tickets, $37.50 less than if he had bought the tickets at the regular price. What was the regular ticket price? paid: $60.00 discount: $37.50 regular: $97.50 $ / ticket tickets $4.00 15 $6.50 $97.50 15 15 9. The expression (3x − 4y2)(3x + 4y2) is equivalent to: 3x 4 y 3x 4 y 3x 3x 3x 4 y 4 y 3x 4 y 4 y 2 2 2 9 x2 12 xy 2 12 xy 2 16 y 4 9 x2 16 y 4 2 2 2 10. A rectangle has an area of 32 square feet and a perimeter of 24 feet. What is the shortest of the side lengths, in feet, of the rectangle? 6 8 A = 32 P = 24 6 4 6 4 6 8 P 24 length 6 24 8 width 6 4 Area 36 32 11. In ΔABC, the sum of the measures of ∠A and ∠B is 47°. What is the measure of ∠C ? B C 47 180 C 133 A C C 12. In the school cafeteria, students choose their lunch from 3 sandwiches, 3 soups, 4 salads, and 2 drinks. How many different lunches are possible for a student who chooses exactly 1 sandwich, 1 soup, 1 salad, and 1 drink? I start EVERY "combination problem" with a simple example like this: Suppose you just had two items: Item A has 2 choices (large or small) Item B has 3 choices: (hats, coats, gloves) The General Rule multiply the number of objects in the sets. 3 sandwiches, 3 soups, 4 salads, and 2 drinks Item A 2 choices a b Item B 3 choices a,1 b,1 1 2 a,2 b,2 3 a,3 b,3 ` Combinations: 3 3 4 2 72 THEREFORE: When there are 2 and 3 choices, there are 6 combinations. 12b. In the school cafeteria, students choose their lunch from 3 sandwiches, 3 soups, 4 salads, and 2 drinks. How many different lunches are possible for a student who chooses exactly 1 sandwich, 1 soup, 1 salad, and 1 drink? This happens very quick, once you get use to it! A B a 1 b 2 3 The problem has 3, 3, 2, and 4 items. with 2 & 3 in a set, I get 6. Therefore, I multiply ... ` Combinations: 3 3 4 2 72 13. For 2 consecutive integers, the result of adding the smaller integer and triple the larger integer is 79. What are the 2 integers? A. 18, 19 B. 19, 20 C. 20, 21 D. 26, 27 Sometimes, it helps to start E. 39, 40 the answers: with smaller =s bigger =b 3×b s + (3 × b) 18 19 57 75 almost 19 20 60 79 yes 13. For 2 consecutive integers, the result of adding the smaller integer and triple the larger integer is 79. What are the 2 integers? A. 18, 19 B. 19, 20 C. 20, 21 D. 26, 27 E. 39, 40 Suppose the two integers are n and n+1 Also, smaller + (3 × bigger) = 79 smaller + (3 × bigger) = n 3 n 1 ` n 3 n 1 79 n 3n 3 79 4n 3 79 4n 76 n 19 14. A function f(x) is defined as f(x) = −8x2. What is f(−3) ? f x 8x 2 f 3 8 3 8 9 72 2 15. If 3x = 54, then which of the following must be true? A. 1 < x < 2 B. 2 < x < 3 C. 3 < x < 4 D. 4 < x < 5 E. 5 < x 31 3 32 9 33 27 3 81 4 3 x 4 54