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### Grade 8 - Mathematics2.12 Direct Proportion - I

 Two variables are in direct proportion to one another if they are always in the same ratio. If two variables x and y are vary in such a way that their ratio x/y is a constant(k). Then x and y are said to vary directly or in direct variation "k" is called the constant of variation. \ If variables x and y are directly then x/y = k or x=ky. This is denoted by x¥y. Example: y¥x, and constant of variation is 6. Find y, when x=3, find x, when y=24. Solution: Since y¥x, we have y = kx But k = 6 Þ y = 6x If x = 3 Þ y = 6*3 = 18 If y = 25 Þ 25 = 3x Þ x = 25/3. Example: If 4 bottles of milk cost \$2, how many bottles can you buy for \$8? Solution: You can write this in proportion as 4:2 :: x:8 or 4/2 = x/8 Cross multiplying we get 2x = 32 x = 16 Answer: 16 bottles Directions: Solve the following problems. Also write atleast 10 examples of your own.
 Q 1: Ken's car uses 20 gallons of gas to drive 425 miles. At this rate, approximately how many gallons of gas will he need for a trip of 1275 miles?90406030 Q 2: If 18 tonnes of grass is needed for 12 cattle. How many tonnes of grass is required for 30 cattle.35 tonnes45 tonnes25 tonnes40 tonnes Q 3: On a map, 1/2 inch = 10 miles. How many miles apart are two towns that are 3 1/4 inches apart on the map?67724554 Q 4: The cost of 10 books is \$80. Find the value of 15 books.\$150\$160\$250\$120 Q 5: y is directly proportional to x, and constant of variation is 15. Find x, when y = 30.4None of these26 Q 6: The toll on the Intercoastal Thruway is 8 cents for every 5 miles traveled. What is the toll for the trip of 115 miles on this road? (Hint: You are comparing cents with miles.)\$1.80\$2\$2.33\$0.60 Q 7: Monthly expenditure of a family of 4 members is \$2,800, what is the expenditure if there are 3 members in a family.\$2,800\$1,600None of these\$2,100 Q 8: y is directly proportional to x, and constant of variation is 8. Find y when x=5.None of these304056 Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!