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DIRECT LINEAR VARIATION
1. If y varies directly with x, and the constant of variation is k = 5, find y when x = 40. Answer: y = 200
2. If y varies directly with x, and the constant of variation is k = ⅓, find y when x = 45.
Answer: y = 15 3. If y varies directly with x, and y = 64 when x = 8, find y when x = 12. Answer: y = 96 4. If y varies directly with x, and y = 72 when x = 6, find y when x = 2. Answer: y = 24
5.
= 9
. Find the constant of variation if v varies directly with w. Answer: k=9 6.
= 9
. Find the constant of variation if w varies directly with v. Answer: k=
.
1
.
7. 2z─
.
11
= 0
. Find the constant of variation if z varies directly with x. Answer: k=
122
8. 2z─
11
= 0
. Find the constant of variation if x varies directly with z. Answer: k=22 9. 3u=5t. Find the constant of variation if u varies directly with t. Answer: k=
53
10. 3u=5t. Find the constant of variation if t varies directly with u. Answer: k=
35
11. The variable y varies directly with z. The value of y is 45 when z=3. Find the constant of variation (k). Answer: k=15 12. The variable a varies directly with n. The value of m is 81 when n is 3. Find the constant of variation (k). Answer: k=27 13. The variable p varies directly with q. The value of p is 27 when q is 63. Find the constant of variation (k). Answer: k=
37
14. The variable x varies directly with y. The value of x200 when y=4. Write an equation that relates x and y. Answer: x=50y 15. The variable c varies directly with d. The value of c=144 when d=6. Write an equation that relates c and d. Answer: c=24d 16. The variable a varies directly with b. The value of a=6.4 when b=2. Write an equation that relates a and b. Answer: a=3.2b 17. The variable y varies directly with x. The value of y is 24 when x is 8. Write an equation that relates x and y. Answer: y=3x 18. The variable y varies directly with x. The value of y is 24 when x is 8. Find the value of y when x=5. Answer: y=15 19. The variable t varies directly with s. The value of t is 15 when s =3. Write an equation that relates s and t. Answer: t=5s 20. The variable t varies directly with s. The value of t is 15 when s=3. Find the value of s when t=25. Answer: s=5 21. Trailblazers Inc. is known for making high quality suits. If they take 9 days to stitch 90 suits, how long will it take them to complete an order of 180 suits? Answer: 18 days 22. Shaun eats six egg whites a day with a protein content of 21.6 grams. Calculate his protein intake, if he consumes 9 egg whites a day. Answer: 32.4 grams
23. Acela Express, the fastest train between Washington D.C and Boston covers a distance of 455 miles in 7 hours. How many miles will the train travel in 4 hours? Answer: 260 miles
24. Mr. Green landed at JFK airport and exchanged €700 for
$854 at a currency exchange store. He realized that he would need more cash and exchanged
€400 more.
How many dollars did he receive for the second transaction? Answer: $488 25. If y varies directly as x, and x=9 when y=15, find y when x=33. Answer: y=55 26. If y varies directly as y, and x=9 when y=6, find x when y=15. Answer: x=45/2 27. If y varies directly as x and given y=9 when x=5, find the equation connection x and y. Answer: y=
5
x 28. If y varies directly as x and given y=9 when x=5, find the value y when x=15. Answer: y=27 29. If y varies directly as x and given y=9 when x=5, find the value x when y=6. Answer: x=10/9 or 3 1/3 30. The cost of a taxi fare (C) varies directly as the distance (D) travelled. When the distance is 60 km, the cost is P35. Find the cost when the distance is 95 km. Answer: 55.42 31. If P varies directly as Q and the value of P is 60 and Q is 40, what is the equation that describes this direct variation of P and Q? Answer: P=
32
Q 32. If a car runs at a constant speed and takes 3 hrs to run a distance of 180 km, what time it will take to run 100 km? Answer:
53
hrs or 1 hr 40 mins 33. The value of y varies directly with x, and y=20 when x=2. Find y when x=8. Answer: y=80. 34. The amount of money raised at a school fundraiser is directly proportional to the number of people who attend. Last year, the amount of money raised for 100 attendees was P2500. How much money will be raised if 1000 people attend this year? Answer: P25000 35. Brady bought an energy efficient washing machine for her new apartment. If she saves about 10 gallons of water per load, how many gallons of water will she save if she washes 20 loads of laundry? Answer: y=200 36. The weight of object on Earth varies directly as its weight on the moon. If a rock weighed 5 pounds on the moon and 30 pounds on Earth, what would be the weight on Earth of a larger rock weighing 26 pounds on the moon? Answer: 156 pounds 37. The amount of money raised at a charity fundraiser is directly proportional to the number of attendees. The amount of money raised for five attendees was P100. How much money will be raised for 60 attendees? Answer: P1200 38. The distance Catelyn travels is directly proportional to the time she spends on the road. If Catelyn spends 5 hours on the road, she travels 30 miles. How far will she go if she only spends 3 hours on the road? Answer: 18 miles
39. If y varies directly as x, and x=12 when y=9, what is the equation that describes this direct variation? Answer: y=
34
x 40. If y varies directly as x, and the constant variation is k is
23
. What is y when x=9? Answer: y=6 41. If y varies directly as x, and y=15 when x=10, then what is y when x=6? Answer: y=9 42. If y varies directly as x, and y=3 when x=15, write an equation describing the variation. Answer: y=
15
x 43. If r varies directly as q, and r=10 when q=6, write an equation describing the variation. Answer: r=
53
q 44. If y varies directly as x, and the constant is 3, what is y when x=7? Answer: y=21 45. If y varies directly as x, and the constant of variation is
54
, what is x when y=5? Answer: x=4 46. If y varies directly as x, and y=6 when x=8, what is y when x=14? Answer: y=
212
47. If y varies directly as x, and y=5when x=4, what is x when y=15? Answer: x=12 48. y varies directly as x. If x=5 when y=12, find x when y=30. Answer: x=
252
49. A dishwasher uses 65 gallons of water to wash 5 loads of dishes. How many gallons of water would be used to wash 12 loads? Answer: 156 gallons 50. Suppose y varies directly as x, and y=16 when x=8. Find y when x=16. Answer: y=32
https://www.shmoop.com/rational-functions/inverse-rational-variation-exercises.html https://www.mathworksheets4kids.com/direct-inverse-variation/constant-equation-l1-1.pdf http://www.mesacc.edu/~scotz47781/mat120/notes/variation/direct/direct_practice.html https://www.mesacc.edu/~scotz47781/mat120/notes/variation/direct/direct.html https://www.onlinemathlearning.com/direct-variation.html https://www.math-only-math.com/direct-variation-problems.html https://www.shelovesmath.com/algebra/beginning-algebra/direct-inverse-and-joint-variation/ https://www.chegg.com/homework-help/solve-direct-variation-problem-see-exampleexamplesuppose-y-v-chapter-7.9-problem-32ss-solution-9781111567668-exc https://math.info/Algebra/Word_Probs_Direct_Variation/ https://study.com/academy/practice/quiz-worksheet-direct-and-inverse-variation-problems.html https://www.sparknotes.com/math/algebra1/variation/section1/ http://www.ps78.com/homeconnect/wp-content/uploads/2016/10/Investigation-3-Worksheet-II-Direct-Variation.pdf https://www.anderson5.net/cms/lib02/SC01001931/Centricity/Domain/2147/Direct%20Variation%20Worksheets.pdf

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