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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.
Q 1: 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.)
$0.60
$1.80
$2
$2.33

Q 2: If 18 tonnes of grass is needed for 12 cattle. How many tonnes of grass is required for 30 cattle.
40 tonnes
45 tonnes
25 tonnes
35 tonnes

Question 3: This question is available to subscribers only!

Question 4: This question is available to subscribers only!


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