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Date:___________________

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Grade 8 - Mathematics
2.12 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 xy.
Example:
yx, and constant of variation is 6. Find y, when x=3, find x, when y=24.

Solution:
Since yx, we have y = kx
But k = 6 y = 6x
If x = 3 y = 6*3 = 18
If y = 25 25 = 3x 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.

Name: ___________________

Date:___________________

Grade 8 - Mathematics
2.12 Direct Proportion - I

Q 1: y is directly proportional to x, and constant of variation is 15. Find x, when y = 30.
4
2
None of these
6

Q 2: The cost of 10 books is $80. Find the value of 15 books.
$160
$150
$120
$250

Q 3: y is directly proportional to x, and constant of variation is 4. Find x, when y = 5.
4/5
46
None of these
5/4

Q 4: y is directly proportional to x, and constant of variation is 8. Find y when x=5.
40
56
None of these
30

Q 5: 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
$2,100
$1,600
None of these

Q 6: y is directly proportional to x, and constant of variation is 7. Find y, when x = 4.
48
28
38
None of these

Q 7: 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?
67
54
72
45

Q 8: 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.)
$2.33
$1.80
$2
$0.60

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Question 10: This question is available to subscribers only!


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