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### Grade 8 - Mathematics2.10 Inverse Proportion - I

 If two variables x and y vary such that xy = constant(k). Then x and y are said to vary inversely or are in inverse variation. If y varies inversely x, then directly as 1/x. And x varies directly as 1/y. Or, if x and y vary inversely, then x ¥ 1/y or y ¥ 1/x. Example: x is varies inversely y and constant of variation is 1/2, find x when y = 5, find y when x = 1/4. Solution: Since x is varies inversely y We have x.y = k, given that k = 1/2. \ xy = 1/2 If y = 5 Þ x.5 = 1/2 Þ x = 1/10. If x = 1/4 Þ 1/4 . y = 1/2 Þ y 1/2 * 4 = 2 Example: If 3 men can paint a house in 2 days, how long will it take 2 men to do the same job?. Solution: This is an inverse relationship. The fewer men, the more days it will take to paint the house. 3:2 :: 2:x or 3/2 = 2/x Cross multiplying 3x = 4 x = 4/3 = 1 1/3 Answer: 1 1/3 days Directions: Solve the following problems. Also write at least 10 examples of your own.
 Q 1: A field can be plowed by 8 machines in 6 hours. If 5 machines are broken and cannot be used, how many hours will it take to plow the field?10 1/27 2/39 3/58 Q 2: A gear with 20 teeth revolving at 200 revolutions per minute is meshed with a second gear turning at 250 revolutions per minute. How many teeth does this gear have?16181225 Q 3: You have enough milk to feed 90 children for 4 days. If 10 of the children do not drink milk, how many days will the supply last?3 1/862 3/44 1/2 Q 4: x is varies inversely y and constant of variation is 2/3, find x when y = 7.2/2121221/2 Q 5: x is varies inversely y and constant of variation is 7/5, find x when y = 7.5None of these1/51 Q 6: x is varies inversely y and constant of variation is 7, find y when x = 9.7/99/779 Q 7: Two boys weighing 60 pounds and 80 pounds balance a seesaw. How many feet from the fulcrum must the heavier boy sit if the lighter boy is 8 feet from the fulcrum? (Hint: Weight times distance from fulcrum remains constant.)65128 Q 8: x is varies inversely y and constant of variation is 5/2, find y when x = 7.55/1414/514 Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!