Make the following comparisons and interpret each one.
1. Compare 16 paintings and 2 artists by:
Subtraction:
Division:
Is your answer for part (b) an example of a ratio or a rate? Explain your answer.
2. Compare 18 books and 6 books by:
Subtraction:
Division:
Is your answer for part (b) an example of a ratio or a rate? Explain your answer.
3. Is 5/13 an example of a ratio or a rate? Explain your answer.
4. Write 14pencils/2people in the form “a to b.” Reduce if possible.
5. Describe the proportion using words.
12movies/3nights = 4movies/1night
6. Find the missing factor.
1.5/7 = x/21
7. Express the sentence as a proportion and solve for x.
16 cups are to 1 gallon as x cups are to 5 gallons.
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?
9. A bottle of children’s liquid fever medicine says the dose for children under 12 is 1/8teaspoon for every 10 pounds your child weighs. If your child weighs 40 pounds, how much medicine should be given?
10. Convert 1% to a fraction and a decimal.
11. Convert 14/4 to a decimal and percent.
12. Convert 400/40 to a decimal and percent. =
13. Convert 14/5% to a fraction.
14. Convert 43/16% to a 4-place decimal.
For questions 15-20, write an equation for each problem and solve.
15. A pearl ring is on sale for 15% off the regular price. The discounted price of the ring is $353.60. What was the original price of the ring?
16. A computer is advertised at $1,285 and you pay $1,366.60. What percent tax are you paying?
17. If you get 91% on a test with 133 questions, how many did you miss? Round your answer to the nearest whole number.
18. 78 is what percent of 65?
19. 7.2 is 16% of what number?
20. What is 115% of 40?
Specify the number of terms and factors in each expression, then list them.
8cf
21. Terms:
22. Factors:
5m + 3n
23. Terms:
24. Factors:
25. Solve 6x + 4y2 + 3 (x=2, y=3)
26. Solve 2 [ -5 – 6(3x – 4y) ] (x=4, y= -1)
Combine like terms.
27. 5x + 14y – 3z – x + 2y
28. (-7+4)m – (15-2)m + |-2|m
State whether each of the following is an equation or an expression.
29. 4x + 17
30. 15 = 3y -16
31. (2x+14y)/20
Solve.
32. 18k + 4 = 6k – 32
33. y + 3.171 = 5.42
Solve.
34. 1/3x = 40
35. 16a/6= 8
36. 7/(x+1)= 21/(x-1)
37. a=bcd solve for d
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.
39. A number less the opposite of negative thirteen is twenty-four.
40. Four times a number increased by five is equal to six times the number decreased by nine.
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.)
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?
43. Your grandma is six less than six times your age. If your grandma is 72, how old are you?
44. Three people are sitting next to each other on a bench. The person in the middle is twice as old as the person to his left and 10 years younger than the person on his right. Their combined ages is 85. How old is the person in the middle?