application 2

MAT-105: APPLIED LIBERAL ARTS MATHEMATICS /48 = % Application Assignment 2 Answer each question and show all work. Make the following comparisons and interpret each one. 1. Compare 16 paintings and 2 artists by: a. Subtraction: 16-2=14 b. Division:16/2=8 c. Is your answer for part (b) an example of a ratio or a rate? Explain your answer. Rate, different units 2. Compare 18 books and 6 books by: a. Subtraction: 18-6=12 b. Division:18/6=3 c. Is your answer for part (b) an example of a ratio or a rate? Explain your answer. Ratio, same units. 3. Is 5 13 an example of a ratio or a rate? Explain your answer. This is a ratio because the denominator isn’t one. 4. Write 14 pencils 2 people in the form “a to b.” Reduce if possible. 14 pencils to 2 people 14 to 2 7 to 1 7 pencils for every person 7 pencils/person 14 pencils for every 2 people 14 pencils/2 people 5. Describe the proportion using words.

12 movies 3 nights = 4 movies 1 night 12 movies for 3 nights 6. Find the missing factor. 1.5 7 = x 21 1.5x3= 4.5 7x3= 21 4.5 7. Express the sentence as a proportion and solve for x . 16 cups are to 1 gallon as x cups are to 5 gallons. 16 c 1 g = xc 5 g 16(5)=1x x=80 cups 8. The ratio of green candies to red candies in a bag is 3:2. If there are 42 green candies, how many red candies are there? Green to red 3 ¿ ¿ 2 ¿ ¿ = 42 ¿ ¿ x ¿ ¿ 3 to 2 3x14 x=28 red candies 2x14 9. A bottle of children’s liquid fever medicine says the dose for children under 12 is 1 8 teaspoon for every 10 pounds your child weighs. If your child weighs 40 pounds, how much medicine should be given? 1 / 8 tsp 10 pounds = x 40 pounds 1 8 x 4 1 = 4 8 = 1 2 If your child weighs 40 pounds they should have ½ teaspoon of medicine.

1285 x 1285 = 1,366.60 1285 x= 1.06 (rounded) You pay a 6% sales tax. 17. If you get 91% on a test with 133 questions, how many did you miss? Round your answer to the nearest whole number. 91 100 = x 133 100 x 100 = 12103 100 133-121=12 You got 121 correct, which means you got 12 wrong. 18. 78 is what percent of 65? 78 65 = x 100 7800 65 = 65 x 65 x=120 78 is 120% of 65 19. 7.2 is 16% of what number? 7.2 x = 16 100 16 x 16 = 720 16 x=45 7.2 is 16% of 45 20. What is 115% of 40? x 40 = 115 100 4600 100 = 100 x 100 x= 46 115% of 40 is 46. Specify the number of terms and factors in each expression, then list them. 8cf 21. Terms: 8cf has 1 term (nothing is being added together) 22. Factors: 8cf has 3 factors (8 x c x f) 5m + 3n 23. Terms: 5m + 3n has 2 terms (5m + 3n) 24. Factors: 2 factors (5 x m, 3 x n)

25. Solve 6x + 4y 2 + 3 (x=2, y=3) 6x+4y 2 +3 6(2)+ 4(3) 2 +3 12+4(9)+3 12+36+3 51 26. Solve 2 [ -5 - 6(3x - 4y) ] (x=4, y= -1) 2 [ -5 - 6(3x - 4y) ] 2 [ -5 - 6(3(4) - 4(-1) ] 2 [ -5 - 6(12 +4) ] 2 [ -5 - 6(16) ] 2 [ -5 - 96 ] 2 [ -101 ] = -202 Combine like terms. 27. 5x + 14y - 3z - x + 2y 5x + 14y - 3z - x + 2y 4x+16y-32 28. (-7+4) m - (15-2) m + | − 2 | m (-7+4) m - (15-2) m + | − 2 | m -3m-13m+2m -16+2m -14m State whether each of the following is an equation or an expression. 29. 4x + 17 Expression (no equal sign) 30. 15 = 3y -16 Equation (has an equal sign)

7x-7= 21x+21 -7x -7x -7=14x+21 -21 -21 -28=14x 14 14 x=-2 37. a=bcd solve for d a bc = bcd bc d= a bc Translate the phrase or sentence into a mathematical equation and solve. 38. Four more than nine times a number is sixteen less than five times the same number. 9x+4=5x-16 x=-5 9x+4=5x-16 -5x -5x 4x+4=-16 -4 -4 4x=-20 4 4 x=-5 39. A number less the opposite of negative thirteen is twenty-four. x-(-13)=24 x=11 x-(-13)=24 x+13=24 -13 -13 x=11 40. Four times a number increased by five is equal to six times the number decreased by nine. 4X+5=6X-9 X=7 4x+5=6x-9 -4x -4x 5=2x-9

+9 +9 14=2x x=7 Solve. Be sure to show your work. 41. If you pay $1,494.93 for a TV that was on sale for 10% off with 6.75% sales tax, what was the original price of the TV? (Sales tax is calculated after the discount is taken.) Final price is 1494.93 6.75% sales tax sales get added. 1.0675 x 1.0675 = 1494.93 1.0675 $1400.12 before sales tax *number is rounded* 1400.12 .90 = .90 x .90 10% discount is 90% of price Discount is subtracted $1555.69 original price of tv *number is rounded* 42. Natalie is trying to figure out whether she can afford to buy a new car. She has the following regular monthly bills: rent $355, utilities $40, phone $25, car insurance $60, food $120, gas $50. Her new car payment will be $240. She makes $13 per hour and 15% is taken out for taxes. If she works the same number of hours each week and there are 4 weeks in each month, what is the minimum number of full hours Natalie would need to work per week to be able to afford the new car? 21hrs/ a week Expenses: 355+40+25+60+120+50=$650 New car would be an additional 240. 650+240= $890 Expenses total: $890 $13hr, 15% taken out for taxes so 11.05 hr (13(.85)= $11.05 Same # of hours each week 4 weeks in each month 890 11.05 = 11.05 x 11.05 x= 80.5 81/4= 21 hours a week (20.25) You need 890$/month to pay for everything CHECK 21 hrs/ a week x 4= 84hrs 84 x 11.05= 928.20 20 hours would give you 884.